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September  2006, 16(3): 513-523. doi: 10.3934/dcds.2006.16.513

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

Lucio Boccardo 1, , Luigi Orsina 2, and  Ireneo Peral 3,

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, Italy
3. 

Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain

Received  January 2006 Revised  July 2006 Published  August 2006

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: 46E3.
Citation: Lucio Boccardo, Luigi Orsina, Ireneo Peral. A remark on existence and optimal summability of solutions of elliptic problems involving Hardy potential. Discrete & Continuous Dynamical Systems - A, 2006, 16 (3) : 513-523. doi: 10.3934/dcds.2006.16.513
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