On the potential theory of some systems of coupled PDEs

Commentationes mathematicae Universitatis Carolinae

Abderrahim Aslimani¹ 

关键词: harmonic function;    superharmonic function;    potential;    elliptic linear differential operator;    kernel;    coupled PDEs system;    Kato measure;   

DOI  :  10.14712/1213-7243.2015.165

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type $L_1u =-\mu_1v$, $L_2v =-\mu_2u$, on a domain $D$ of $\mathbb R^d$, where $\mu_1$ and $\mu_2$ are suitable measures on~$D$, and $L_1$, $L_2$ are two second order linear differential elliptic operators on~$D$ with coefficients of class~$\mathcal C^\infty$. We also obtain the integral representation of the nonnegative solutions and supersolutions of the system (S) by means of the Green kernels and Martin boundaries associated with $L_1$ and $L_2$, and a convergence property for increasing sequences of solutions of~(S).

【 授权许可】

CC BY