Improved Rellich inequalities for the polyharmonic operator

Details Improved Rellich inequalities for the polyharmonic operator Improved Rellich inequalities for the polyharmonic operator

2005-02-14

arxiv.org/abs/math/0502286v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

We prove two improved versions of the Hardy-Rellich inequality for the polyharmonic operator $(-\Delta)^m$ involving the distance to the boundary. The first involves an infinite series improvement using logarithmic functions, while the second contains $L^2$ 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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