Wolfgang Arendt, Reiner Schätzle
Published 2010-10-08Version 1
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.
On the Kato problem for elliptic operators in non-divergence form
Weighted mixed-norm $L_p$ estimates for equations in non-divergence form with singular coefficients: the Dirichlet problem
Higher Order Convergence Rates in Theory of Homogenization I: Equations of Non-divergence Form
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