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Archiv der Mathematik

, Volume 81, Issue 5, pp 548–558 | Cite as

The Laplacian on \( C(\overline \Omega) \) with generalized Wentzell boundary conditions

Original paper

Abstract.

In this note we prove that the Laplacian with generalized Wentzell boundary conditions on an open bounded regular domain Ω in \( \mathbb{R}^m \) defined by

\( (1)\qquad {\cal A}f := \Delta f,\quad D(A) := \left \{ f \in C^{1}_{n} (\overline \Omega) : \Delta f \in C(\overline \Omega);\; \Delta f + \beta \frac {\partial f} {\partial n} + \gamma f = 0\; {\rm on}\; \partial\Omega \right \} \) generates an analytic semigroup of angle \( \frac{\pi}{2} \) on \( C(\overline \Omega) \) for every β > 0 and \( \gamma \in C(\partial\Omega) \) (for the definition of \( C^{1}_{n} (\overline \Omega) \) cf. (1.3)).

Mathematics Subject Classification (1991):

47D06 34G10 35K05 

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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di L’AquilaRoio Poggio (AQ)Italy

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