Weighted Inequalities And Degenerate Elliptic Partial Differential Equations
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Weighted Inequalities And Degenerate Elliptic Partial Differential Equations
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Author : E.W. Stredulinsky
language : en
Publisher: Springer
Release Date : 2006-12-08
Weighted Inequalities And Degenerate Elliptic Partial Differential Equations written by E.W. Stredulinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Weighted Inequalities And Degenerate Elliptic Partial Differential Equations
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Author : Edward W. Stredulinsky
language : en
Publisher:
Release Date : 1984
Weighted Inequalities And Degenerate Elliptic Partial Differential Equations written by Edward W. Stredulinsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
Various weighted inequalities and weighted function spaces relevant to degenerate partial differential equations are studied. The results are applied to degenerate second order divergence form elliptic equations and systems to establish continuity of weak solutions. The methods used allow the consideration of very general classes of weights. In particular the weights are characterized for several Sobolev inequalities in terms of weighted capacities, a theorem is proven for weighted reverse Holder inequalities and a continuity estimate is established for certain weighted Sobolev spaces. (Author).
Weighted Sobolev Spaces And Degenerate Elliptic Equations
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Author : Albo Carlos Cavalheiro
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2023-09-29
Weighted Sobolev Spaces And Degenerate Elliptic Equations written by Albo Carlos Cavalheiro and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-29 with Mathematics categories.
In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is disturbed in the sense that some degeneration or singularity appears. This bad behavior can be caused by the coefficients of the corresponding differential operator as well as by the solution itself. There are several very concrete problems in various practices which lead to such differential equations, such as glaciology, non-Newtonian fluid mechanics, flows through porous media, differential geometry, celestial mechanics, climatology, and reaction-diffusion problems, among others. This book is based on research by the author on degenerate elliptic equations. This book will be a useful reference source for graduate students and researchers interested in differential equations.
Harmonic Analysis Partial Differential Equations And Applications
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Author : Sagun Chanillo
language : en
Publisher: Birkhäuser
Release Date : 2017-02-20
Harmonic Analysis Partial Differential Equations And Applications written by Sagun Chanillo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-20 with Mathematics categories.
This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm inequalities for classical operators like Singular integrals, fractional integrals and maximal functions that arise in Harmonic Analysis. Other papers deal with applications of Harmonic Analysis to Degenerate Elliptic equations, variational problems, Several Complex variables, Potential theory, free boundaries and boundary behavior of functions.
Degenerate Elliptic Equations
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Author : Serge Levendorskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Degenerate Elliptic Equations written by Serge Levendorskii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.
Nonlinear Potential Theory And Weighted Sobolev Spaces
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Author : Bengt O. Turesson
language : en
Publisher: Springer
Release Date : 2007-05-06
Nonlinear Potential Theory And Weighted Sobolev Spaces written by Bengt O. Turesson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
Nonlinear Potential Theory Of Degenerate Elliptic Equations
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Author : Juha Heinonen
language : en
Publisher: Courier Dover Publications
Release Date : 2018-05-16
Nonlinear Potential Theory Of Degenerate Elliptic Equations written by Juha Heinonen and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-16 with Mathematics categories.
A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.
Potential Theory And Degenerate Partial Differential Operators
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Author : Marco Biroli
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Potential Theory And Degenerate Partial Differential Operators written by Marco Biroli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Recent years have witnessed an increasingly close relationship growing between potential theory, probability and degenerate partial differential operators. The theory of Dirichlet (Markovian) forms on an abstract finite or infinite-dimensional space is common to all three disciplines. This is a fascinating and important subject, central to many of the contributions to the conference on `Potential Theory and Degenerate Partial Differential Operators', held in Parma, Italy, February 1994.
Weighted Inequalities In Lorentz And Orlicz Spaces
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Author : Vakhtang Kokilashvili
language : en
Publisher: World Scientific
Release Date : 1991-12-31
Weighted Inequalities In Lorentz And Orlicz Spaces written by Vakhtang Kokilashvili and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-12-31 with Mathematics categories.
This book is intended as a survey of latest results on weighted inequalities in Lorentz, Orlicz spaces and Zygmund classes. During the last few years they have become one of the mostdeveloped offshoots of the theory of the harmonic analysis operators. Up to now there has been no monograph devoted to these questions, the results are mostly scattered in various journals and a part of the book consists of results not published anywhere else. Many of theorems presented have only previously been published in Russian. Contents:Integral Operators in Nonweighted Orlicz ClassesMaximal Functions and Potentials in Weighted Orlicz ClassesSingular Integrals in Weighted Orlicz ClassesIntegral Operators in Weighted Zygmund ClassesFractional Maximal Function in Weighted Lorentz SpacesPotentials and Riesz Transforms in Weighted Lorentz Spaces Readership: Mathematicians, graduate students and researchers in real and complex analysis. keywords:Orlicz Space;Lorentz Space;Zygmund Space;Weighted Space;Ap Weight;Maximal Operator;Riesz Potential;Hilbert Transform;Singular Integral;Weighted Inequalities “The authors, together with various collaborators, have made important contributions to the field over the last decade … The exposition is clear with detailed proofs of all statements and the monograph will certainly be a good supplement to survey articles and books on the weighted inequalities.” Mathematical Reviews
Mathematical Inequalities
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Author : B. G. Pachpatte
language : en
Publisher: Elsevier
Release Date : 2005-05-04
Mathematical Inequalities written by B. G. Pachpatte and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-04 with Mathematics categories.
The book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics. * It contains a variety of inequalities which find numerous applications in various branches of mathematics.* It contains many inequalities which have only recently appeared in the literature and cannot yet be found in other books.* It will be a valuable reference for someone requiring a result about inequalities for use in some applications in various other branches of mathematics.* Each chapter ends with some miscellaneous inequalities for futher study.* The work will be of interest to researchers working both in pure and applied mathematics, and it could also be used as the text for an advanced graduate course.