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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 2, 2000, pp. 369–380
DOI: 10.4171/ZAA/956

Published online: 2000-06-30

Sobolev Inequalities on Sets with Irregular Boundaries

Tero Kilpeläinen[1] and Jan Malý[2]

(1) University of Jyväskylä, Finland
(2) Charles University, Praha, Czech Republic

We derive (weighted) Sobolev-Poincaré inequalities for $s$-John domains and $s$-cusp domains, both with optimal exponents. These results are obtained as consequences of a more comprehensive criterion.

Keywords: Sobolev inequality, Poincaré inequality, embeddings, weighted Sobolev spaces, John domains, cusp domains

Kilpeläinen Tero, Malý Jan: Sobolev Inequalities on Sets with Irregular Boundaries. Z. Anal. Anwend. 19 (2000), 369-380. doi: 10.4171/ZAA/956