Compactness of the embedding operators for rough domains

Vladimir Gol'dshtein; Alexander G. Ramin

Compactness of the embedding operators for rough domains

Vladimir Gol'dshtein
, Alexander G. Ramin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

New classes of non-smooth bounded domains D, for which the embedding operator from II¹(D) into L²(D) is compact, are introduced. These classes include, in particular, the domains whose boundary locally are graphs of C- functions, but also contain much larger classes of domains. Examples of non-smooth domains for which the above embedding is compact are given. Applications to scattering by rough obstacles arc mentioned.

Original language	English
Pages (from-to)	127-141
Number of pages	15
Journal	Mathematical Inequalities and Applications
Volume	4
Issue number	1
State	Published - 1 Jan 2001

Keywords

Embedding theorems
Quasiconformal mappings
Rough domains
Sobolev spaces

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Cite this

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title = "Compactness of the embedding operators for rough domains",

abstract = "New classes of non-smooth bounded domains D, for which the embedding operator from II1(D) into L2(D) is compact, are introduced. These classes include, in particular, the domains whose boundary locally are graphs of C- functions, but also contain much larger classes of domains. Examples of non-smooth domains for which the above embedding is compact are given. Applications to scattering by rough obstacles arc mentioned.",

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AU - Gol'dshtein, Vladimir

AU - Ramin, Alexander G.

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N2 - New classes of non-smooth bounded domains D, for which the embedding operator from II1(D) into L2(D) is compact, are introduced. These classes include, in particular, the domains whose boundary locally are graphs of C- functions, but also contain much larger classes of domains. Examples of non-smooth domains for which the above embedding is compact are given. Applications to scattering by rough obstacles arc mentioned.

AB - New classes of non-smooth bounded domains D, for which the embedding operator from II1(D) into L2(D) is compact, are introduced. These classes include, in particular, the domains whose boundary locally are graphs of C- functions, but also contain much larger classes of domains. Examples of non-smooth domains for which the above embedding is compact are given. Applications to scattering by rough obstacles arc mentioned.

KW - Embedding theorems

KW - Quasiconformal mappings

KW - Rough domains

KW - Sobolev spaces

UR - https://www.scopus.com/pages/publications/0347121843

M3 - Article

AN - SCOPUS:0347121843

SN - 1331-4343

VL - 4

SP - 127

EP - 141

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 1

ER -

Compactness of the embedding operators for rough domains

Abstract

Keywords

ASJC Scopus subject areas

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