96-85 Davies E.B., Hinz A.M.

Explicit constants for Rellich inequalities in $L^p(\Omega)$ (33K, Latex) Mar 21, 96

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Abstract. We obtain explicit and sometimes sharp constants for weighted Rellich and Hardy inequalities in $L_p(\Omega)$ where $\Omega$ stands for Euclidean space or a bounded region in a complete Riemannian manifold. The application of Rellich inequalities to the study of relative bounds of a potential with respect to $(-\Delta)^m$ in $L_p(\Omega)$ is facilitated by showing the purely local character of the determination of these bounds. The proof for this fact is based on a special partition of unity. The final section is then devoted to a detailed analysis of potentials with local singularities, and best constants for Rellich and Hardy inequalities are obtained.

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