Existence of Solutions to Poisson's Equation

Canadian mathematical bulletin

关键词: semi-infinity interval;    vector $p$-Laplacian;    multivalued nonlinear;    fixed point index;    Hartman condition;    completely continuous map;   

DOI  :  10.4153/CMB-2008-024-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $Omega$ be a domain in $mathbb R^n$ ($ngeq 2$). We find anecessary and sufficient topological condition on $Omega$ suchthat, for any measure $mu$ on $mathbb R^n$, there is a function $u$with specified boundary conditions that satisfies the Poissonequation $Delta u=mu$ on $Omega$ in the sense of distributions.

【 授权许可】

Unknown