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Isoperimetric Inequalities and Imbedding Theorems in Irregular Domains
Author(s) -
Hajłasz Piotr,
Koskela Pekka
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006346
Subject(s) - isoperimetric inequality , mathematics , boundary (topology) , fractal , compact space , pure mathematics , isoperimetric dimension , inequality , mathematical analysis
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.