Differentiable functions on bad domains
著者
書誌事項
Differentiable functions on bad domains
World Scientific, c1997
- : hbk
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注記
Includes bibliographical references (p. 461-475) and index
内容説明・目次
内容説明
The spaces of functions with derivatives in Lp, called the Sobolev spaces, play an important role in modern analysis. During the last decades, these spaces have been intensively studied and by now many problems associated with them have been solved. However, the theory of these function classes for domains with nonsmooth boundaries is still in an unsatisfactory state.In this book, which partially fills this gap, certain aspects of the theory of Sobolev spaces for domains with singularities are studied. We mainly focus on the so-called imbedding theorems, extension theorems and trace theorems that have numerous applications to partial differential equations. Some of such applications are given.Much attention is also paid to counter examples showing, in particular, the difference between Sobolev spaces of the first and higher orders. A considerable part of the monograph is devoted to Sobolev classes for parameter dependent domains and domains with cusps, which are the simplest non-Lipschitz domains frequently used in applications.This book will be interesting not only to specialists in analysis but also to postgraduate students.
目次
- Part 1 Sobolev spaces for good or general domains: density theorems, extension theorems and Poincare's inequality for Sobolev functions
- imbedding theorems of Sobolev type and their applications
- imbedding theorems and isoperimetric inequalities. Part 2 Sobolev spaces for domains singularly depending on parameters: extension of functions defined on parameter dependent domains
- traces of functions with first derivatives on parameter dependent components of a boundary. Part 3 Sobolev spaces for domains with cusps: extension of functions to the exterior of a domain with the vertex of a peak on the boundary
- imbedding theorems for Sobolev spaces in domains with cusps
- traces of functions in Sobolev spaces on the boundary of a domain with a cusp.
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