A remark on existence and optimal summability of solutions of elliptic problems involving Hardy potential

Lucio Boccardo; Luigi Orsina; Ireneo Peral

doi:10.3934/dcds.2006.16.513

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2006, Volume 16, Issue 3: 513-523. Doi: 10.3934/dcds.2006.16.513

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A remark on existence and optimal summability of solutions of elliptic problems involving Hardy potential

1.
Dipartimento di Matematica, Università di Roma 1, Piazza A. Moro 2, 00185 Roma
2.
Dipartimento di Matematica Universitµa di Roma I, Piazza A. Moro 2, 00185 Roma
3.
Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid

Received: December 31, 2005

Revised: June 30, 2006

Published: August 2006

Abstract Related Papers Cited by

Abstract

We study the effect of a zero order term on existence and optimal summability of solutions to the elliptic problem

$ -\text{div}( M(x)\nabla u)- a\frac{u}{|x|^2}=f \text{ in } \Omega, \qquad u=0 \text{ on } \partial \Omega$,

with respect to the summability of $f$ and the value of the parameter $a$. Here $\Omega$ is a bounded domain in $\mathbb{R}^N$ containing the origin.

Keywords:

Laplace equation,
Hardy potential summability of solution.

Mathematics Subject Classification: Primary: 35J05, 35J25; Secondary: 46E35.

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