The Laplacian with Wentzell-Robin Boundary Conditions on Spaces of Continuous Functions |
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| Authors: | W. Arendt G. Metafune D. Pallara S. Romanell |
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| Affiliation: | (1) Abteilung Angewandte Analysis Universitat Ulm D - 89069 Ulm, Germany;(2) Dipartimento di Matematica, !["ldquo"]("/content/klh3qgeffvj3c5d6/xlarge8220.gif") E. De Giorgi!["rdquo"]("/content/klh3qgeffvj3c5d6/xlarge8221.gif") Universita degli Studi di Lecce, Via Provinciale Lecce-Arnesano I - 73100 Lecce, Italy;(3) Dipartimento Interuniversitario di Matematica, Universita degli Studi di Bari - Campus Via E. orabona 4 I - 70125 Bari, Italy |
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| Abstract: | We investigate the Laplacian  on a smooth bounded open set  Rn with Wentzell-Robin boundary condition $beta u+frac{partial u}{partial nu} + Delta u=0$ on the boundary  . Under the assumption  $memb$ C() with $geq$ 0 , we prove that generates a differentiable positive contraction semigroup on $C(bar{Omega})$ and study some monotonicity properties and the asymptotic behaviour. |
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