Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations Quasilinear Elliptic Singular Problems

Author : Veron Laurent
Publisher : World Scientific
Page : 476 pages
File Size : 41,8 Mb
Release : 2017-05-05
Category : Mathematics
ISBN : 9789814730341

Get Book

Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations: Quasilinear Elliptic Singular Problems by Veron Laurent Pdf

This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects: The existence of separable singular solutions enables the description of isolated singularities of general solutions. The construction of singular solutions is delicate and cannot be done without the understanding of the spherical p-harmonic eigenvalue problem.When the equations are considered on a Riemannian manifold, existence or non-existence of solutions depends on geometric assumptions such as the curvature. A priori estimates and Liouville type problems are analyzed.When the equations are considered with a forcing term in the class of measures, their study is strongly linked to the properties of a class of potentials appearing in harmonic analysis such as the Riesz, the Bessel or the Wolff potentials and to their associated capacities. Necessary and sufficient conditions for existence of solutions link the continuity of the measure with respect to some appropriate capacity.

Author : Laurent Veron
Publisher : World Scientific Publishing Company
Page : 457 pages
File Size : 46,7 Mb
Release : 2016-09-30
Category : Mathematics
ISBN : 9814730327

Get Book

Local and Global Aspects of Quasilinear Degenerate Elliptic Equations by Laurent Veron Pdf

This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects: The existence of separable singular solutions enables the description of isolated singularities of general solutions. The construction of singular solutions is delicate and cannot be done without the understanding of the spherical p-harmonic eigenvalue problem. When the equations are considered on a Riemannian manifold, existence or non-existence of solutions depends on geometric assumptions such as the curvature. A priori estimates and Liouville type problems are analyzed. When the equations are considered with a forcing term in the class of measures, their study is strongly linked to the properties of a class of potentials appearing in harmonic analysis such as the Riesz, the Bessel or the Wolff potentials and to their associated capacities. Necessary and sufficient conditions for existence of solutions link the continuity of the measure with respect to some appropriate capacity.

Author : A. V. Ivanov
Publisher : American Mathematical Soc.
Page : 306 pages
File Size : 46,6 Mb
Release : 1984
Category : Mathematics
ISBN : 0821830805

Get Book

Quasilinear Degenerate and Nonuniformly Elliptic and Parabolic Equations of Second Order by A. V. Ivanov Pdf

Author : J. P. Gossez,Denis Bonheure
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 43,9 Mb
Release : 2011
Category : Differential equations, Elliptic
ISBN : 9780821849071

Get Book

Nonlinear Elliptic Partial Differential Equations by J. P. Gossez,Denis Bonheure Pdf

This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium. The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the $p$-Laplacian operator, the antimaximum principle, the Fucik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.

Author : Emanuel Indrei,Diego Marcon,Levon Nurbekyan
Publisher : American Mathematical Society
Page : 148 pages
File Size : 44,8 Mb
Release : 2023-01-09
Category : Mathematics
ISBN : 9781470466527

Get Book

Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs by Emanuel Indrei,Diego Marcon,Levon Nurbekyan Pdf

This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February 28–March 1, 2021, and hosted by Purdue University, West Lafayette, IN. The mathematical content of this volume is at the intersection of viscosity theory, Fourier analysis, mass transport theory, fractional elliptic theory, and geometric analysis. The reader will encounter, among others, the following topics: the principal-agent problem; Maxwell's equations; Liouville-type theorems for fully nonlinear elliptic equations; a doubly monotone flow for constant width bodies; and the edge dislocations problem for crystals that describes the equilibrium configurations by a nonlocal fractional Laplacian equation.

Author : W.-M. Ni,L.A. Peletier,James Serrin
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461396086

Get Book

Nonlinear Diffusion Equations and Their Equilibrium States II by W.-M. Ni,L.A. Peletier,James Serrin Pdf

In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.

Author : Pavel Drábek,Alois Kufner,Francesco Nicolosi
Publisher : Walter de Gruyter
Page : 233 pages
File Size : 44,7 Mb
Release : 2011-07-22
Category : Mathematics
ISBN : 9783110804775

Get Book

Quasilinear Elliptic Equations with Degenerations and Singularities by Pavel Drábek,Alois Kufner,Francesco Nicolosi Pdf

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.

Author : Peter Lindqvist
Publisher : Unknown
Page : 12 pages
File Size : 45,6 Mb
Release : 1990
Category : Differential equations, Elliptic
ISBN : 9512204649

Get Book

Global Integrability and Degenerate Quasilinear Elliptic Equations by Peter Lindqvist Pdf

Author : Laurent Veron
Publisher : CRC Press
Page : 396 pages
File Size : 46,5 Mb
Release : 1996-08-01
Category : Mathematics
ISBN : 0582035392

Get Book

Singularities of Solutions of Second-Order Quasilinear Equations by Laurent Veron Pdf

This text examines the singularity problem for solutions of elliptic and parabolic quasilinear equations of second order.

Author : Ravi P. Agarwal,Kanishka Perera
Publisher : Hindawi Publishing Corporation
Page : 1268 pages
File Size : 49,7 Mb
Release : 2006
Category : Difference equations
ISBN : 9775945380

Get Book

Proceedings of the Conference on Differential & Difference Equations and Applications by Ravi P. Agarwal,Kanishka Perera Pdf

Author : Dorothee Haroske,Thomas Runst,Hans-Jürgen Schmeisser
Publisher : Birkhäuser
Page : 462 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880350

Get Book

Function Spaces, Differential Operators and Nonlinear Analysis by Dorothee Haroske,Thomas Runst,Hans-Jürgen Schmeisser Pdf

This volume is dedicated to our teacher and friend Hans Triebel. The core of the book is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA--01) held in Teistungen, Thuringia / Germany, from June 28 to July 4,2001, in honour of his 65th birthday. This was the fifth in a series of meetings organised under the same name by scientists from Finland (Helsinki, Oulu) , the Czech Republic (Prague, Plzen) and Germany (Jena) promoting the collaboration of specialists in East and West, working in these fields. This conference was a very special event because it celebrated Hans Triebel's extraordinary impact on mathematical analysis. The development of the mod ern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics is deeply influenced by his lasting contributions. In a series of books Hans Triebel has given systematic treatments of the theory of function spaces from different points of view, thus revealing its interdependence with interpolation theory, harmonic analysis, partial differential equations, nonlinear operators, entropy, spectral theory and, most recently, anal ysis on fractals. The presented collection of papers is a tribute to Hans Triebel's distinguished work. The book is subdivided into three parts: • Part I contains the two invited lectures by O.V. Besov (Moscow) and D.E. Edmunds (Sussex) having a survey character and honouring Hans Triebel's contributions.

Author : Michel Chipot,Pavol Quittner
Publisher : Elsevier
Page : 630 pages
File Size : 46,5 Mb
Release : 2006-08-08
Category : Mathematics
ISBN : 0080463827

Get Book

Handbook of Differential Equations: Stationary Partial Differential Equations by Michel Chipot,Pavol Quittner Pdf

This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Key features: - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics

Author : Anatoly Golberg,Peter Kuchment,David Shoikhet
Publisher : Springer Nature
Page : 319 pages
File Size : 50,7 Mb
Release : 2023-04-26
Category : Mathematics
ISBN : 9783031254246

Get Book

Harmonic Analysis and Partial Differential Equations by Anatoly Golberg,Peter Kuchment,David Shoikhet Pdf

Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Author : Michail Borsuk,Vladimir Kondratiev
Publisher : Elsevier
Page : 538 pages
File Size : 52,7 Mb
Release : 2006-01-12
Category : Mathematics
ISBN : 0080461735

Get Book

Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains by Michail Borsuk,Vladimir Kondratiev Pdf

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. Key features: * New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. * The question about the influence of the coefficients smoothness on the regularity of solutions. * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems. * The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian. * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. * The question about the influence of the coefficients smoothness on the regularity of solutions. * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems. * The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian. * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

Author : Anonim
Publisher : Unknown
Page : 1770 pages
File Size : 45,6 Mb
Release : 2004
Category : Mathematics
ISBN : UVA:X006180633

Get Book

Mathematical Reviews by Anonim Pdf