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arXiv · 1209.0588

Weighted Hardy inequalities beyond Lipschitz domains

Juha Lehrbäck
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Abstract

It is a well-known fact that in a Lipschitz domain \Omega\subset R^n a p-Hardy inequality, with weight d(x,\partial\Omega)^\beta, holds for all u\in C_0^\infty(\Omega) whenever \beta<p-1. We show that actually the same is true under the sole assumption that the boundary of the domain satisfies a uniform density condition with the exponent \lambda=n-1. Corresponding results also hold for smaller exponents, and, in fact, our methods work in general metric spaces satisfying standard structural assumptions.

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BibTeXRIS

Juha Lehrbäck. 2012-09-04. Weighted Hardy inequalities beyond Lipschitz domains. https://doi.org/10.1090/s0002-9939-2014-11904-6

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