Studies in Potential Theory and Function 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 Studies in Potential Theory and Function Spaces write by Torbjörn Kolsrud. This book was released on 1983. Studies in Potential Theory and Function Spaces available in PDF, EPUB and Kindle.
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
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.
Integral Representation Theory
Integral Representation 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 Integral Representation Theory write by Jaroslav Lukeš. This book was released on 2010. Integral Representation Theory available in PDF, EPUB and Kindle. This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications
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 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.
