Local solvability of high order elliptic equations

M.A MUSCHIETTI ,F. TOURNIER

Filadelfia

Seminario; Coloquium of mathematics of Temple University; 2017

Temple University

We consider $2m^{th}$ order elliptic equations with Holder coefficients. We show local solvability of the Dirichlet problem with $m$ conditions on the boundary of the upper half space. First we consider local solvability in free space and then we treat the boundary case. Our method is based on applying the operator to an approximate solution and iteration in the Holder spaces. A priori estimates for the approximate solution is the essential part of the paper.