Issue Math. Model. Nat. Phenom. Volume 3, Number 7, 2008 Special issue dedicated to Glenn Webb Page(s) 143 - 147 DOI 10.1051/mmnp:2008046 Published online 23 October 2008

Math. Model. Nat. Phenom. Vol. 3, No. 7, 2008, pp. 143-147
DOI: 10.1051/mmnp:2008046

Wentzell Boundary Conditions in the Nonsymmetric Case

A. Favini¹, G. R. Goldstein², J. A. Goldstein² and S. Romanelli<sup>3

1</sup>  Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5 40126 Bologna, Italy
²  Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152
³  Dipartimento di Matematica, Universit`a degli Studi di Bari, via E. Orabona 4, 70125 Bari, Italy

favini@dm.unibo.it

Published online: 23 October 2008

Abstract
Let L be a nonsymmetric second order uniformly elliptic operator with generalWentzell boundary conditions. We show that a suitable version of L generates a quasicontractive semigroup on an L^p space that incorporates both the underlying domain and its boundary. This extends the earlier work of the authors on the symmetric case.

Mathematics Subject Classification. 47D06, 47B44, 35K20

Key words: Wentzell boundary conditions -- nonsymmetric elliptic operators -- C₀ semigroups -- quasidissipative operators

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