Nonlinear Potential Theory and Weighted Sobolev Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Potential Theory and Weighted Sobolev Spaces write by Bengt O. Turesson. This book was released on 2007-05-06. Nonlinear Potential Theory and Weighted Sobolev Spaces available 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 and Weighted Sobolev Spaces
Nonlinear Potential Theory and Weighted Sobolev Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Potential Theory and Weighted Sobolev Spaces write by Bengt Ove Turesson. This book was released on 1995. Nonlinear Potential Theory and Weighted Sobolev Spaces available in PDF, EPUB and Kindle.
Nonlinear Potential Theory of Degenerate Elliptic Equations
Nonlinear Potential Theory of Degenerate Elliptic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Potential Theory of Degenerate Elliptic Equations write by Juha Heinonen. This book was released on 2018-05-16. Nonlinear Potential Theory of Degenerate Elliptic Equations available 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.
Nonlinear Potential Theory on Metric Spaces
Nonlinear Potential Theory on Metric Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Potential Theory on Metric Spaces write by Anders Björn. This book was released on 2011. Nonlinear Potential Theory on Metric Spaces available in PDF, EPUB and Kindle. The $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.
Function Spaces and Potential Theory
Function Spaces and Potential Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Function Spaces and Potential Theory write by David R. Adams. This book was released on 2012-12-06. Function Spaces and Potential Theory available in PDF, EPUB and Kindle. "..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society
