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

Lucio Boccardo | Zendy; Luigi Orsina | Zendy; Ireneo Peral | Zendy

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

Author(s) -

Lucio Boccardo,

Luigi Orsina,

Ireneo Peral

Publication year - 2006

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2006.16.513

Subject(s) - nabla symbol , omega , bounded function , domain (mathematical analysis) , order (exchange) , mathematics , zero (linguistics) , pure mathematics , combinatorics , mathematical analysis , physics , philosophy , quantum mechanics , linguistics , finance , economics

\begin{abstract} We study the effect of a zero order term on existence and optimal summability of solutions to the elliptic problem $$ -\text{div}( M(x)\nabla u)- a\dfrac{u}{|x|^2}=f \hbox{ in } \Omega\,, \qquad u=0 \hbox{ on } \partial \Omega\,, $$ 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. \end{abstract

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