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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

  • K.-J. Engel
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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