Semigroups Generated by Elliptic Operators in Non-Divergence Form on $C_0(/omega)$

Details Semigroups Generated by Elliptic Operators in Non-Divergence Form on $C_0(/omega)$ Semigroups Generated by Elliptic Operators in Non-Divergence Form on $C_0(/omega)$

2010-10-08

arxiv.org/abs/1010.1703v1

Mathematics

Analysis of PDEs

Scientific paper

Given a bounded domain in the Euclidean space satisfying the uniform outer cone condition, we show that a uniformly elliptic operator of second order with continuous second order coefficients generates a holomorphic semigroup on the space of all continuous functions vanishing at the boundary. In particular, Lipschitz domains are allowed. This result was so far known under considerable stronger regularity assumptions. Also the Dirichlet problem is considered for such operators.

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