Questions tagged [dirichlet-problem]

I was wondering if any of you had ever encountered operators on $L^2(\mathbb{R}^2)$ of the form $$ \nabla \cdot (A(x)\nabla) $$ where $A(x)$ is some symmetric matrix field (viewed as $L^2(\mathbb{R}^{...

As the title asks. Let me elaborate; suppose $\mathcal K$ is a continuum (compact, connected) set of $\mathbb C$ (with at least two points!). Let's say that $g(z;a)$ is the green's function of the ...