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 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.
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.
Studies in Potential Theory and Function Spaces
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.
Potential Theory on Harmonic Spaces
Potential Theory on Harmonic 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 Potential Theory on Harmonic Spaces write by Corneliu Constantinescu. This book was released on 2012-01-16. Potential Theory on Harmonic Spaces available in PDF, EPUB and Kindle. There has been a considerable revival of interest in potential theory during the last 20 years. This is made evident by the appearance of new mathematical disciplines in that period which now-a-days are considered as parts of potential theory. Examples of such disciplines are: the theory of Choquet capacities, of Dirichlet spaces, of martingales and Markov processes, of integral representation in convex compact sets as well as the theory of harmonic spaces. All these theories have roots in classical potential theory. The theory of harmonic spaces, sometimes also called axiomatic theory of harmonic functions, plays a particular role among the above mentioned theories. On the one hand, this theory has particularly close connections with classical potential theory. Its main notion is that of a harmonic function and its main aim is the generalization and unification of classical results and methods for application to an extended class of elliptic and parabolic second order partial differential equations. On the other hand, the theory of harmonic spaces is closely related to the theory of Markov processes. In fact, all important notions and results of the theory have a probabilistic interpretation.
