A note on the Rellich formula in Lipschitz domains

Autores: Alano Ancona
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 42, Nº 1, 1998, págs. 223-237
Idioma: inglés
DOI: 10.5565/publmat_42198_12
Títulos paralelos:
- Una nota sobre la fórmula de Rellich en dominios de Lipschitz
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Resumen
- Let $L$ be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain $\Omega$ of $\Bbb R^N$ and having Lipschitz coefficients in $\Omega$. It is shown that the Rellich formula with respect to $\Omega$ and $L$ extends to all functions in the domain $\Cal D=\{u \in H_0^1(\Omega);\, L(u) \in L^2(\Omega)\}$ of $L$. This answers a question of A. Chaïra and G. Lebeau