Some Connections Between Isoperimetric And Sobolev Type Inequalities

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Some Connections between Isoperimetric and Sobolev-type Inequalities

Serguei Germanovich Bobkov,Christian Houdré
Some Connections between Isoperimetric and Sobolev type Inequalities Book PDF

Author : Serguei Germanovich Bobkov,Christian Houdré
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 54,7 Mb
Release : 1997
Category : Gaussian processes
ISBN : 9780821806425

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Some Connections between Isoperimetric and Sobolev-type Inequalities by Serguei Germanovich Bobkov,Christian Houdré Pdf

For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.

Some Connections Between Isoperimetric and Sobolev-Type Inequalities

Serguei Germanovich Bobkov
Some Connections Between Isoperimetric and Sobolev Type Inequalities Book PDF

Author : Serguei Germanovich Bobkov
Publisher : Oxford University Press, USA
Page : 127 pages
File Size : 48,8 Mb
Release : 2014-09-11
Category : Gaussian processes
ISBN : 1470402017

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Some Connections Between Isoperimetric and Sobolev-Type Inequalities by Serguei Germanovich Bobkov Pdf

For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.

Concentration, Functional Inequalities and Isoperimetry

Christian Houdré
Concentration Functional Inequalities and Isoperimetry Book PDF

Author : Christian Houdré
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 46,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821849712

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Concentration, Functional Inequalities and Isoperimetry by Christian Houdré Pdf

The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, with recent new applications in random matrices and information theory. This will appeal to graduate students and researchers interested in the interplay between analysis, probability, and geometry.

Special Functions, Partial Differential Equations, and Harmonic Analysis

Constantine Georgakis,Alexander M. Stokolos,Wilfredo Urbina
Special Functions Partial Differential Equations and Harmonic Analysis Book PDF

Author : Constantine Georgakis,Alexander M. Stokolos,Wilfredo Urbina
Publisher : Springer
Page : 248 pages
File Size : 49,8 Mb
Release : 2014-11-07
Category : Mathematics
ISBN : 9783319105451

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Special Functions, Partial Differential Equations, and Harmonic Analysis by Constantine Georgakis,Alexander M. Stokolos,Wilfredo Urbina Pdf

This volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to stimulate further research in the future in this area of pure and applied mathematics.

Sobolev Spaces

Vladimir Maz'ya
Sobolev Spaces Book PDF

Author : Vladimir Maz'ya
Publisher : Springer Science & Business Media
Page : 882 pages
File Size : 49,8 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9783642155642

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Sobolev Spaces by Vladimir Maz'ya Pdf

Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.

European Congress of Mathematics

Ari Laptev
European Congress of Mathematics Book PDF

Author : Ari Laptev
Publisher : European Mathematical Society
Page : 906 pages
File Size : 46,9 Mb
Release : 2005
Category : Mathematics
ISBN : 3037190094

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European Congress of Mathematics by Ari Laptev Pdf

The European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris, 1992, Budapest, 1996, and Barcelona, 2000, the Fourth European Congress of Mathematics took place in Stockholm, Sweden, June 27 to July 2, 2004, with 913 participants from 65 countries. Apart from seven plenary and thirty three invited lectures, there were six Science Lectures covering the most relevant aspects of mathematics in science and technology. Moreover, twelve projects of the EU Research Training Networks in Mathematics and Information Sciences, as well as Programmes from the European Science Foundation in Physical and Engineering Sciences, were presented. Ten EMS Prizes were awarded to young European mathematicians who have made a particular contribution to the progress of mathematics. Five of the prizewinners were independently chosen by the 4ECM Scientific Committee as plenary or invited speakers. The other five prizewinners gave their lectures in parallel sessions. Most of these contributions are now collected in this volume, providing a permanent record of so much that is best in mathematics today.

One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances

Sergey Bobkov,Michel Ledoux
One Dimensional Empirical Measures Order Statistics and Kantorovich Transport Distances Book PDF

Author : Sergey Bobkov,Michel Ledoux
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 43,5 Mb
Release : 2019-12-02
Category : Education
ISBN : 9781470436506

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One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances by Sergey Bobkov,Michel Ledoux Pdf

This work is devoted to the study of rates of convergence of the empirical measures μn=1n∑nk=1δXk, n≥1, over a sample (Xk)k≥1 of independent identically distributed real-valued random variables towards the common distribution μ in Kantorovich transport distances Wp. The focus is on finite range bounds on the expected Kantorovich distances E(Wp(μn,μ)) or [E(Wpp(μn,μ))]1/p in terms of moments and analytic conditions on the measure μ and its distribution function. The study describes a variety of rates, from the standard one 1n√ to slower rates, and both lower and upper-bounds on E(Wp(μn,μ)) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.

Around the Research of Vladimir Maz'ya I

Ari Laptev
Around the Research of Vladimir Maz ya I Book PDF

Author : Ari Laptev
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 51,6 Mb
Release : 2009-12-02
Category : Mathematics
ISBN : 9781441913418

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Around the Research of Vladimir Maz'ya I by Ari Laptev Pdf

The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented new results and reviews from world-recognized specialists. Sobolev type spaces, extensions, capacities, Sobolev inequalities, pseudo-Poincare inequalities, optimal Hardy-Sobolev-Maz'ya inequalities, Maz'ya's isocapacitary inequalities in a measure-metric space setting and many other actual topics are discussed.

Approaching the Kannan-Lovász-Simonovits and Variance Conjectures

David Alonso-Gutiérrez,Jesús Bastero
Approaching the Kannan Lov sz Simonovits and Variance Conjectures Book PDF

Author : David Alonso-Gutiérrez,Jesús Bastero
Publisher : Springer
Page : 159 pages
File Size : 46,6 Mb
Release : 2015-01-07
Category : Mathematics
ISBN : 9783319132631

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Approaching the Kannan-Lovász-Simonovits and Variance Conjectures by David Alonso-Gutiérrez,Jesús Bastero Pdf

Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovász-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the treated topics. Offering a presentation suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, giving the interested reader rapid access to the core of these conjectures. In addition, four recent and important results in this theory are presented in a compelling way. The first two are theorems due to Eldan-Klartag and Ball-Nguyen, relating the variance and the KLS conjectures, respectively, to the hyperplane conjecture. Next, the main ideas needed prove the best known estimate for the thin-shell width given by Guédon-Milman and an approach to Eldan's work on the connection between the thin-shell width and the KLS conjecture are detailed.

The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities

George Xian-Zhi Yuan
The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities Book PDF

Author : George Xian-Zhi Yuan
Publisher : American Mathematical Soc.
Page : 157 pages
File Size : 46,8 Mb
Release : 1998
Category : Maxima and minima
ISBN : 9780821807477

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The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities by George Xian-Zhi Yuan Pdf

This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.

Hodge Theory in the Sobolev Topology for the de Rham Complex

Luigi Fontana,Steven George Krantz,Marco M. Peloso
Hodge Theory in the Sobolev Topology for the de Rham Complex Book PDF

Author : Luigi Fontana,Steven George Krantz,Marco M. Peloso
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 53,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821808306

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Hodge Theory in the Sobolev Topology for the de Rham Complex by Luigi Fontana,Steven George Krantz,Marco M. Peloso Pdf

In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L^2$ topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. It features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems; theorems completely explained and proved; and new geometric tools for differential analysis on domains and manifolds.

The Defect Relation of Meromorphic Maps on Parabolic Manifolds

George Lawrence Ashline
The Defect Relation of Meromorphic Maps on Parabolic Manifolds Book PDF

Author : George Lawrence Ashline
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 46,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821810699

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The Defect Relation of Meromorphic Maps on Parabolic Manifolds by George Lawrence Ashline Pdf

This book is intended for graduate students and research mathematicians working in several complex variables and analytic spaces.

Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems

Hasna Riahi
Study of the Critical Points at Infinity Arising from the Failure of the Palais Smale Condition for n Body Type Problems Book PDF

Author : Hasna Riahi
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 51,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821808733

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Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems by Hasna Riahi Pdf

In this work, the author examines the following: When the Hamiltonian system $m_i \ddot{q}_i + (\partial V/\partial q_i) (t,q) =0$ with periodicity condition $q(t+T) = q(t),\; \forall t \in \mathfrak R$ (where $q_{i} \in \mathfrak R^{\ell}$, $\ell \ge 3$, $1 \le i \le n$, $q = (q_{1},...,q_{n})$ and $V = \sum V_{ij}(t,q_{i}-q_{j})$ with $V_{ij}(t,\xi)$ $T$-periodic in $t$ and singular in $\xi$ at $\xi = 0$) is posed as a variational problem, the corresponding functional does not satisfy the Palais-Smale condition and this leads to the notion of critical points at infinity. This volume is a study of these critical points at infinity and of the topology of their stable and unstable manifolds. The potential considered here satisfies the strong force hypothesis which eliminates collision orbits. The details are given for 4-body type problems then generalized to n-body type problems.

Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory

Roland Speicher
Combinatorial Theory of the Free Product with Amalgamation and Operator Valued Free Probability Theory Book PDF

Author : Roland Speicher
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 43,8 Mb
Release : 1998
Category : Combinatorial analysis
ISBN : 9780821806937

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Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory by Roland Speicher Pdf

Free probability theory, introduced by Voiculescu, has developed very actively in the last few years and has had an increasing impact on quite different fields in mathematics and physics. Whereas the subject arose out of the field of von Neumann algebras, presented here is a quite different view of Voiculescu's amalgamated free product. This combinatorial description not only allows re-proving of most of Voiculescu's results in a concise and elegant way, but also opens the way for many new results. Unlike other approaches, this book emphasizes the combinatorial structure of the concept of ``freeness''. This gives an elegant and easily accessible description of freeness and leads to new results in unexpected directions. Specifically, a mathematical framework for otherwise quite ad hoc approximations in physics emerges.

Treelike Structures Arising from Continua and Convergence Groups

Brian Hayward Bowditch
Treelike Structures Arising from Continua and Convergence Groups Book PDF

Author : Brian Hayward Bowditch
Publisher : American Mathematical Soc.
Page : 86 pages
File Size : 43,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821810033

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Treelike Structures Arising from Continua and Convergence Groups by Brian Hayward Bowditch Pdf

This book is intended for graduate students and research mathematicians working in group theory and generalizations