We derive (weighted) Sobolev-Poincaré inequalities for -John domains and -cusp domains, both with optimal exponents. These results are obtained as consequences of a more comprehensive criterion.
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Tero Kilpeläinen, Jan Malý, Sobolev Inequalities on Sets with Irregular Boundaries. Z. Anal. Anwend. 19 (2000), no. 2, pp. 369–380DOI 10.4171/ZAA/956