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Keywords:
Hardy inequality; Rellich type inequality; Bessel function; Lamb constant; distance function; Laplace operator
Hardy inequality; Rellich type inequality; Bessel function; Lamb constant; distance function; Laplace operator
Summary:
Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain one-dimensional Hardy type inequalities and their multidimensional analogues in convex domains with the finite inradius. We use Bessel functions and the Lamb constant. The statements proved are a generalization for the case of arbitrary $p\geq 2$ of the corresponding inequality proved by F. G. Avkhadiev, K.-J. Wirths (2011) for $p = 2$. Also we establish Rellich type inequalities on arbitrary domains, regular sets, on domains with $\theta $-cone condition and on convex domains.
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