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.
- ISBN10 0471903671
- ISBN13 9780471903673
- Publish Date 15 May 1985
- Publish Status Out of Print
- Out of Print 5 December 1996
- Publish Country GB
- Publisher John Wiley and Sons Ltd
- Imprint John Wiley & Sons Ltd
- Edition Licensed ed.
- Format Hardcover
- Pages 116
- Language English