Applications of change of variables operators for exact embedding theorems

V. Gol'dshtein, L. Gurov

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

We propose here a new method for the investigation of embedding operators. It is based on an exact description of classes of homeomorphisms that induce change of variables operators on the Sobolev spaces. This method permits to obtain new exact results about embedding operators Wp1(G){right arrow, hooked}Lq(G) (or C(G)) in domains G ⊂ ℝn with irregular boundaries. For these types of domains the behavior of the limiting embedding exponent q1,G*(p) is very complicated and surprising. We construct classes of simply connected domains with nonsmooth function q1,G*(p) and a class of multiply connected domains with discontinuous function q1,G*(P).

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalIntegral Equations and Operator Theory
Volume19
Issue number1
DOIs
StatePublished - 1 Mar 1994

Keywords

  • MSC 1991: Primary 46E39, Secondary 30C60

Fingerprint

Dive into the research topics of 'Applications of change of variables operators for exact embedding theorems'. Together they form a unique fingerprint.

Cite this