Sobolev spaces: with applications to elliptic partial differential equations

Sobolev spaces play an outstanding role in modern analysis, in particular, inthe 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 interestin 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 ?rst 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 editionis enhanced by many recent results and it includes new applications to linearand nonlinear partial differential equations. New historical comments, five new chapters and a signi?cantly augmented list of references aim to create a broader and modern view of the area. New, expanded and revised edition of Sobolev Spaces, originally published in the Springer Series in Soviet Mathematics (1985) Is enhanced by many recent results New applications to linear and nonlinear partial differential equations are included New historical comments, five new chapters and the signi?cantly augmented list of references aim to create a broader and modern view of the area INDICE: Introduction.- 1 .Basic Properties of Sobolev Spaces.- 2 .Inequalities for Functions Vanishing at the Boundary.- 3.Conductor and Capacitary Inequalities with Applications to Sobolev-type Embeddings.- 4.Generalizations for Functions on Manifolds and Topological Spaces.- 5.Integrability of Functions in the Space L 1/1(?).- 6.Integrability of Functions in the Space L 1/p (?).- 7.Continuity and Boundedness of Functions in Sobolev Spaces.- 8.Localization Moduli of Sobolev Embeddings for General Domains.- 9.Space of Functions of Bounded Variation.- 10.Certain Function Spaces, Capacities and Potentials.- 11 Capacitary and Trace Inequalities for Functions in Rn with Derivatives of an Arbitrary Order.-12.Pointwise Interpolation Inequalities for Derivatives and Potentials.- 13.A Variant of Capacity.- 14.-Integral Inequality for Functions on a Cube.- 15.Embedding of the Space L l/p(?) into Other Function Spaces.- 16.Embedding L l/p(?) ? W m/r(?).-17.Approximation in Weighted Sobolev Spaces.-18.Spectrum of the Schrödinger operator and the Dirichlet Laplacian.- References.- List of Symbols.- Subject Index.- Author Index.

• ISBN: 978-3-642-15563-5
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 840
• Fecha Publicación: 01/12/2010
• Nº Volúmenes: 1
• Idioma: Inglés