Weighted Sobolev spaces
著者
書誌事項
Weighted Sobolev spaces
Wiley, c1985
Licensed ed.
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注記
Translated from the Czech
"A Wiley-Interscience publication."
Bibliography: p. [108]-111
Includes index
内容説明・目次
内容説明
This book deals with some 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 part. The introductory part starts with the fundamental definitions and some motivating examples and proceeds by going through the auxiliary results: weight functions, definition domains, Hardy inequality. Part one is devoted to the study of properties of Sobolev spaces with power-type weights; here the relation to the classical Sobolev spaces, conditions guaranteeing the density of smooth functions, imbedding theorems and some other problems are dealt with. Part two studies analogous problems for weights of a more general type, while the brief concluding Part three concerns applications of weighted spaces to the solution of the Dirichlet problem for an elliptic linear differential operator.
目次
- Introduction
- Motivation
- Weight
- Domain
- Hardy Inequality
- Part One: POWER-TYPE WEIGHTS: Some Elementary Assertions
- Density of Smooth Functions
- Imbedding Theorems
- Miscellaneous
- Part Two: GENERAL WEIGHTS: Several Elementary Results
- Density of Smooth Functions
- Imbedding Theorems
- Part Three: APPLICATIONS: Formulation of the Problem
- Power-Type Weights
- General Weights
- References
- List of Imbeddings
- Index.
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