Solutions of nonlinear differential equations on a Riemannian manifold and their trace on the Martin boundary
Solutions of nonlinear differential equations on a Riemannian manifold and their trace on the Martin boundary
Let $L$ be a second order elliptic differential operator on a Riemannian manifold $E$ with no zero order terms. We say that a function $h$ is $L$-harmonic if $Lh=0$. Every positive $L$-harmonic function has a unique representation \begin{equation*}h(x)=\int _{Eâ} k(x,y) \nu (dy), \end{equation*} where $k$ is the Martin kernel, $Eâ$ …