# American Institute of Mathematical Sciences

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

 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.

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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