Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces

Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces book. This book definitely worth reading, it is an incredibly well-written.

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré
Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces Book PDF

Author : Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré
Publisher : Unknown
Page : 121 pages
File Size : 46,9 Mb
Release : 2019
Category : Differential calculus
ISBN : 1470455137

Get Book

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces by Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré Pdf

Aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, our new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, our new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD*(K,N) condition of Bacher-Sturm.

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré
Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces Book PDF

Author : Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 45,9 Mb
Release : 2020-02-13
Category : Education
ISBN : 9781470439132

Get Book

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces by Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré Pdf

The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.

New Trends on Analysis and Geometry in Metric Spaces

Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam
New Trends on Analysis and Geometry in Metric Spaces Book PDF

Author : Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam
Publisher : Springer Nature
Page : 312 pages
File Size : 41,9 Mb
Release : 2022-02-04
Category : Mathematics
ISBN : 9783030841416

Get Book

New Trends on Analysis and Geometry in Metric Spaces by Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam Pdf

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.

Recent Advances in Alexandrov Geometry

Gerardo Arizmendi Echegaray,Luis Hernández-Lamoneda,Rafael Herrera Guzmán
Recent Advances in Alexandrov Geometry Book PDF

Author : Gerardo Arizmendi Echegaray,Luis Hernández-Lamoneda,Rafael Herrera Guzmán
Publisher : Springer Nature
Page : 119 pages
File Size : 50,8 Mb
Release : 2022-10-27
Category : Mathematics
ISBN : 9783030992989

Get Book

Recent Advances in Alexandrov Geometry by Gerardo Arizmendi Echegaray,Luis Hernández-Lamoneda,Rafael Herrera Guzmán Pdf

This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field. It contains enhanced versions of the lecture notes of the two mini-courses plus those of one research talk given at CIMAT. Peter Petersen’s part aims at presenting various rigidity results about Alexandrov spaces in a way that facilitates the understanding by a larger audience of geometers of some of the current research in the subject. They contain a brief overview of the fundamental aspects of the theory of Alexandrov spaces with lower curvature bounds, as well as the aforementioned rigidity results with complete proofs. The text from Fernando Galaz-García’s minicourse was completed in collaboration with Jesús Nuñez-Zimbrón. It presents an up-to-date and panoramic view of the topology and geometry of 3-dimensional Alexandrov spaces, including the classification of positively and non-negatively curved spaces and the geometrization theorem. They also present Lie group actions and their topological and equivariant classifications as well as a brief account of results on collapsing Alexandrov spaces. Jesús Nuñez-Zimbrón’s contribution surveys two recent developments in the understanding of the topological and geometric rigidity of singular spaces with curvature bounded below.

Nonlinear Diffusion Equations

Zhuoqun Wu
Nonlinear Diffusion Equations Book PDF

Author : Zhuoqun Wu
Publisher : World Scientific
Page : 526 pages
File Size : 48,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9812799796

Get Book

Nonlinear Diffusion Equations by Zhuoqun Wu Pdf

Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations. This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon. Contents: Newtonian Filtration Equations: Existence and Uniqueness of Solutions: One Dimensional Case; Existence and Uniqueness of Solutions: Higher Dimensional Case; Regularity of Solutions: One Dimensional Case; Regularity of Solutions: Higher Dimensional Case; Properties of the Free Boundary: One Dimensional Case; Properties of the Free Boundary: Higher Dimensional Case; Initial Trace of Solutions; Other Problems; Non-Newtonian Filtration Equations: Existence of Solutions; Harnack Inequality and Initial Trace of Solutions; Regularity of Solutions; Uniqueness of Solutions; Properties of the Free Boundary; Other Problems; General Quasilinear Equations of Second Order: Weakly Degenerate Equations in One Dimension; Weakly Degenerate Equations in Higher Dimension; Strongly Degenerate Equations in One Dimension; Degenerate Equations in Higher Dimension without Terms of Lower Order; General Strongly Degenerate Equations in Higher Dimension; Classes BV and BV x; Nonlinear Diffusion Equations of Higher Order: Similarity Solutions of a Fourth Order Equation; Equations with Double-Degeneracy; CahnOCoHilliard Equation with Constant Mobility; CahnOCoHilliard Equations with Positive Concentration Dependent Mobility; Thin Film Equation; CahnOCoHilliard Equation with Degenerate Mobility. Readership: Researchers, lecturers and graduate students in the fields of analysis and differential equations, mathematical physics and fluid mechanics."

Geometric Optics for Surface Waves in Nonlinear Elasticity

Jean-François Coulombel,Mark Williams
Geometric Optics for Surface Waves in Nonlinear Elasticity Book PDF

Author : Jean-François Coulombel,Mark Williams
Publisher : American Mathematical Soc.
Page : 143 pages
File Size : 49,7 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440374

Get Book

Geometric Optics for Surface Waves in Nonlinear Elasticity by Jean-François Coulombel,Mark Williams Pdf

This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as “the amplitude equation”, is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions uε to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength ε, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to uε on a time interval independent of ε. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.

Global Smooth Solutions for the Inviscid SQG Equation

Angel Castro,Diego Cordoba,Javier Gomez-Serrano
Global Smooth Solutions for the Inviscid SQG Equation Book PDF

Author : Angel Castro,Diego Cordoba,Javier Gomez-Serrano
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 40,9 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442149

Get Book

Global Smooth Solutions for the Inviscid SQG Equation by Angel Castro,Diego Cordoba,Javier Gomez-Serrano Pdf

In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.

Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R

Peter Poláčik
Propagating Terraces and the Dynamics of Front Like Solutions of Reaction Diffusion Equations on R Book PDF

Author : Peter Poláčik
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 43,9 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441128

Get Book

Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R by Peter Poláčik Pdf

The author considers semilinear parabolic equations of the form ut=uxx+f(u),x∈R,t>0, where f a C1 function. Assuming that 0 and γ>0 are constant steady states, the author investigates the large-time behavior of the front-like solutions, that is, solutions u whose initial values u(x,0) are near γ for x≈−∞ and near 0 for x≈∞. If the steady states 0 and γ are both stable, the main theorem shows that at large times, the graph of u(⋅,t) is arbitrarily close to a propagating terrace (a system of stacked traveling fonts). The author proves this result without requiring monotonicity of u(⋅,0) or the nondegeneracy of zeros of f. The case when one or both of the steady states 0, γ is unstable is considered as well. As a corollary to the author's theorems, he shows that all front-like solutions are quasiconvergent: their ω-limit sets with respect to the locally uniform convergence consist of steady states. In the author's proofs he employs phase plane analysis, intersection comparison (or, zero number) arguments, and a geometric method involving the spatial trajectories {(u(x,t),ux(x,t)):x∈R}, t>0, of the solutions in question.

Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case

Jacob Bedrossian,Pierre Germain,Nader Masmoudi
Dynamics Near the Subcritical Transition of the 3D Couette Flow I Below Threshold Case Book PDF

Author : Jacob Bedrossian,Pierre Germain,Nader Masmoudi
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 52,6 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442170

Get Book

Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case by Jacob Bedrossian,Pierre Germain,Nader Masmoudi Pdf

The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.

The Riesz Transform of Codimension Smaller Than One and the Wolff Energy

Benjamin Jaye,Fedor Nazarov,Maria Carmen Reguera,Xavier Tolsa
The Riesz Transform of Codimension Smaller Than One and the Wolff Energy Book PDF

Author : Benjamin Jaye,Fedor Nazarov,Maria Carmen Reguera,Xavier Tolsa
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 50,5 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442132

Get Book

The Riesz Transform of Codimension Smaller Than One and the Wolff Energy by Benjamin Jaye,Fedor Nazarov,Maria Carmen Reguera,Xavier Tolsa Pdf

Fix $dgeq 2$, and $sin (d-1,d)$. The authors characterize the non-negative locally finite non-atomic Borel measures $mu $ in $mathbb R^d$ for which the associated $s$-Riesz transform is bounded in $L^2(mu )$ in terms of the Wolff energy. This extends the range of $s$ in which the Mateu-Prat-Verdera characterization of measures with bounded $s$-Riesz transform is known. As an application, the authors give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator $(-Delta )^alpha /2$, $alpha in (1,2)$, in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions.

Conformal Graph Directed Markov Systems on Carnot Groups

Vasileios Chousionis,Jeremy T. Tyson,Mariusz Urbanski
Conformal Graph Directed Markov Systems on Carnot Groups Book PDF

Author : Vasileios Chousionis,Jeremy T. Tyson,Mariusz Urbanski
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 53,9 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442156

Get Book

Conformal Graph Directed Markov Systems on Carnot Groups by Vasileios Chousionis,Jeremy T. Tyson,Mariusz Urbanski Pdf

The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.

Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields

Lisa Berger,Chris Hall,Rene Pannekoek,Rachel Pries,Shahed Sharif
Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields Book PDF

Author : Lisa Berger,Chris Hall,Rene Pannekoek,Rachel Pries,Shahed Sharif
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 54,6 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442194

Get Book

Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields by Lisa Berger,Chris Hall,Rene Pannekoek,Rachel Pries,Shahed Sharif Pdf

The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.

Filtrations and Buildings

Christophe Cornut
Filtrations and Buildings Book PDF

Author : Christophe Cornut
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 45,9 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442217

Get Book

Filtrations and Buildings by Christophe Cornut Pdf

The author constructs and studies a scheme theoretical version of the Tits vectorial building, relates it to filtrations on fiber functors, and uses them to clarify various constructions pertaining to affine Bruhat-Tits buildings, for which he also provides a Tannakian description.

The Mother Body Phase Transition in the Normal Matrix Model

Pavel M. Bleher,Guilherme L. F. Silva
The Mother Body Phase Transition in the Normal Matrix Model Book PDF

Author : Pavel M. Bleher,Guilherme L. F. Silva
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 46,5 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470441845

Get Book

The Mother Body Phase Transition in the Normal Matrix Model by Pavel M. Bleher,Guilherme L. F. Silva Pdf

In this present paper, the authors consider the normal matrix model with cubic plus linear potential.

Affine Flag Varieties and Quantum Symmetric Pairs

Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang
Affine Flag Varieties and Quantum Symmetric Pairs Book PDF

Author : Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 40,7 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470441753

Get Book

Affine Flag Varieties and Quantum Symmetric Pairs by Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang Pdf

The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.