Improved Rellich inequalities for the polyharmonic operator

2005/02/14 by Gerassimos Barbatis, G. Barbatis, Barbatis, G.
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #math.AP #math.SP #msc:26D10 #msc:35J20

paper · pdf · doi:10.48550/arxiv.math/0502286

17 pages

arxiv created 2005/02/14 · arxiv updated 2009/12/01

Abstract

We prove two improved versions of the Hardy-Rellich inequality for the polyharmonic operator (-Δ)^m involving the distance to the boundary. The first involves an infinite series improvement using logarithmic functions, while the second contains L² norms and involves as a coefficient the volume of the domain. We find explicit constants for these inequalities, and we prove their optimality in the first case.

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