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.
![L^p](http://siba-ese.unile.it/plugins/generic/latexRender/cache/49bfb25a6ab05e9068cff109a717c17f.png)
![1<p<\infty](http://siba-ese.unile.it/plugins/generic/latexRender/cache/88a75ba350e7897c55ff37511f1a98f9.png)
DOI Code:
10.1285/i15900932v31n1p103
Keywords:
Degenerate elliptic operators ; Analytic Semigroups
Full Text: PDF