Embedding of Sobolev Spaces and Properties of the Domain

O. V. Besov

Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 343-349.

Résumé

We establish the embedding of the Sobolev space $W_p^s(G)\subset L_q(G)$ for an irregular domain $G$ in the case of a limit exponent under new relations between the parameters depending on the geometric properties of the domain $G$.

Détail

Keywords: Sobolev space, Sobolev embedding theorem, domain with flexible $\sigma$-cone condition, Hölder's inequality, Marcinkiewicz interpolation theorem.

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