Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T09:52:00.607Z Has data issue: false hasContentIssue false
  • English
  • Français

ISOPERIMETRIC INEQUALITIES AND IMBEDDING THEOREMS IN IRREGULAR DOMAINS

Published online by Cambridge University Press:  01 October 1998

PIOTR HAJŁASZ  and
PEKKA KOSKELA
PIOTR HAJŁASZ
Affiliation:
Instytut Matematyki, Uniwersytet Warszawski, Banacha 2, 02-097 Warszawa, Poland. E-mail: [email protected] Present address: Department of Mathematics, University of Jyväskylä, PO Box 35, Fin-40351 Jyväskylä, Finland. E-mail: [email protected]
PEKKA KOSKELA
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
Get access

Abstract

The paper proves several weighted imbedding theorems for domains with fractal boundaries. The weights considered are distances to the boundary to certain powers, and the domains are so-called s-John domains. The paper also proves, in the general setting, that the existence of an imbedding implies compactness of the imbedding for lower exponents. Moreover, following Maz'ya, the paper reformulates the imbedding theorems in the language of local isoperimetric and capacity estimates.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 2 , October 1998 , pp. 425 - 450
Copyright
The London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)