The Hardy-Rellich Inequality for Polyharmonic Operators

Mark P. Owen

The Hardy-Rellich Inequality for Polyharmonic Operators

谱理论 2007-05-23 v1 泛函分析

作者: Mark P. Owen

摘要

The Hardy-Rellich inequality given here generalizes a Hardy inequality of Davies (1984), from the case of the Dirichlet Laplacian of a region $\Omega\subseteq\real^N$ to that of the higher order polyharmonic operators with Dirichlet boundary conditions. The inequality yields some immediate spectral information for the polyharmonic operators and also bounds on the trace of the associated semigroups and resolvents.

关键词

hardy inequalities hardy spaces dirichlet problem

引用

@article{arxiv.math/9803015,
  title  = {The Hardy-Rellich Inequality for Polyharmonic Operators},
  author = {Mark P. Owen},
  journal= {arXiv preprint arXiv:math/9803015},
  year   = {2007}
}

备注

19 pages, 2 diagrams

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