Weighted Sobolev Spaces and Degenerate Elliptic Equations

Weighted Sobolev Spaces and Degenerate Elliptic Equations
Author: Albo Carlos Cavalheiro
Publsiher: Cambridge Scholars Publishing
Total Pages: 333
Release: 2023-09-29
Genre: Mathematics
ISBN: 9781527551671

Download Weighted Sobolev Spaces and Degenerate Elliptic Equations Book in PDF, Epub and Kindle

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.

Weighted Inequalities and Degenerate Elliptic Partial Differential Equations

Weighted Inequalities and Degenerate Elliptic Partial Differential Equations
Author: E.W. Stredulinsky
Publsiher: Springer
Total Pages: 149
Release: 2006-12-08
Genre: Mathematics
ISBN: 9783540389286

Download Weighted Inequalities and Degenerate Elliptic Partial Differential Equations Book in PDF, Epub and Kindle

Weighted Inequalities and Degenerate Elliptic Partial Differential Equations

Weighted Inequalities and Degenerate Elliptic Partial Differential Equations
Author: Edward W. Stredulinsky
Publsiher: Unknown
Total Pages: 142
Release: 1984
Genre: Electronic Book
ISBN: OCLC:227618151

Download Weighted Inequalities and Degenerate Elliptic Partial Differential Equations Book in PDF, Epub and Kindle

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).

Degenerate Elliptic Equations

Degenerate Elliptic Equations
Author: Serge Levendorskii
Publsiher: Springer Science & Business Media
Total Pages: 442
Release: 2013-11-11
Genre: Mathematics
ISBN: 9789401712156

Download Degenerate Elliptic Equations Book in PDF, Epub and Kindle

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

Nonlinear Potential Theory and Weighted Sobolev Spaces
Author: Bengt O. Turesson
Publsiher: Springer
Total Pages: 188
Release: 2007-05-06
Genre: Mathematics
ISBN: 9783540451686

Download Nonlinear Potential Theory and Weighted Sobolev Spaces Book in PDF, Epub and Kindle

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

Nonlinear Potential Theory of Degenerate Elliptic Equations
Author: Juha Heinonen,Tero Kipelainen,Olli Martio
Publsiher: Courier Dover Publications
Total Pages: 417
Release: 2018-05-16
Genre: Mathematics
ISBN: 9780486824253

Download Nonlinear Potential Theory of Degenerate Elliptic Equations Book in PDF, Epub and Kindle

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.

Sobolev Spaces in Mathematics I

Sobolev Spaces in Mathematics I
Author: Vladimir Maz'ya
Publsiher: Springer Science & Business Media
Total Pages: 395
Release: 2008-12-02
Genre: Mathematics
ISBN: 9780387856483

Download Sobolev Spaces in Mathematics I Book in PDF, Epub and Kindle

This volume mark’s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.

Some Applications of Weighted Sobolev Spaces

Some Applications of Weighted Sobolev Spaces
Author: Anna-Margarete Sändig
Publsiher: Springer-Verlag
Total Pages: 264
Release: 2019-06-12
Genre: Technology & Engineering
ISBN: 9783663113850

Download Some Applications of Weighted Sobolev Spaces Book in PDF, Epub and Kindle