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


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 L^p, 1<p<\infty. The proof relies on the discussion of the model case of the half-space and the derivation of the main result via local charts.

DOI Code: 10.1285/i15900932v31n1p103

Keywords: Degenerate elliptic operators ; Analytic Semigroups

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