Some Applications of Weighted Sobolev Spaces
Author: Alois Kufner
Publisher: Vieweg+teubner Verlag
Published: 1987-11
Total Pages: 272
ISBN-13:
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Author: Alois Kufner
Publisher: Vieweg+teubner Verlag
Published: 1987-11
Total Pages: 272
ISBN-13:
DOWNLOAD EBOOKAuthor: Anna-Margarete Sändig
Publisher: Springer-Verlag
Published: 2019-06-12
Total Pages: 264
ISBN-13: 366311385X
DOWNLOAD EBOOKAuthor: Bengt O. Turesson
Publisher: Springer
Published: 2007-05-06
Total Pages: 188
ISBN-13: 3540451684
DOWNLOAD EBOOKThe 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.
Author: Alois Kufner
Publisher:
Published: 1985-07-23
Total Pages: 130
ISBN-13:
DOWNLOAD EBOOKA systematic account of the subject, this book deals with properties and applications of the Sobolev spaces with weights, the weight function being dependent on the distance of a point of the definition domain from the boundary of the domain or from its parts. After an introduction of definitions, examples and auxilliary results, it describes the study of properties of Sobolev spaces with power-type weights, and analogous problems for weights of a more general type. The concluding chapter addresses applications of weighted spaces to the solution of the Dirichlet problem for an elliptic linear differential operator.
Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
Published: 2011-02-11
Total Pages: 882
ISBN-13: 3642155642
DOWNLOAD EBOOKSobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.
Author: Vladimir Maz'ya
Publisher: Springer
Published: 2013-12-21
Total Pages: 506
ISBN-13: 3662099225
DOWNLOAD EBOOKThe Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q
Author: Juha Kinnunen
Publisher: American Mathematical Soc.
Published: 2021-08-02
Total Pages: 354
ISBN-13: 1470465752
DOWNLOAD EBOOKThis book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
Author: Raj Narayan Dhara
Publisher:
Published: 2016
Total Pages:
ISBN-13:
DOWNLOAD EBOOKSłowa kluczowe: weighted Poincare inequality, weighted Orlicz-Sobolev spaces, weighted Orlicz-Slobodetskii spaces, isoperimetric inequalities, weighted Sobolev spaces, $p$-Laplace equation, Baire Category method, extension operator, nonhomogeneous boundaryvalue problem, trace theorem, degenerate elliptic PDEs, upper and lower bounds of eigenvalues, two weighted Poincare inequality, eigenvalue problems, nonexistence.
Author: D. Bahuguna
Publisher: Alpha Science Int'l Ltd.
Published: 2002
Total Pages: 204
ISBN-13: 9781842650943
DOWNLOAD EBOOKThis work covers the Sobolev spaces and their applications to many areas of differential equations. It deals with some basic results on Sobolev spaces, density theorems, and approximation theorems and embedding theorems.
Author: Pankaj Jain
Publisher:
Published: 2000
Total Pages: 19
ISBN-13:
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