Analytic semigroups generated in by elliptic operators with high order degeneracy at the boundary

Abstract

Given a regular bounded domain, we show that an elliptic operator whose diffusion coefficients degenerate at the boundary at least as the square of the distance from the boundary, endowed with a suitable domain, generates an analytic semigroup in , . The proof relies on the discussion of the model case of the half-space and the derivation of the main result via local charts.