A spectral result for Hardy inequalities

2013/02/13 by Devyver, Baptiste
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1302.3039

Abstract

Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. P-W≥0) and best constant α. We give conditions so that the spectrum of W^-1P is [α,∞). We apply this to several well-known Hardy inequalities: (improved) Hardy inequalities on a bounded convex domain with potential involving the distance to the boundary, and Hardy inequalities for minimal submanifolds of the Euclidean space.

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