Electron. J. Diff. Eqns., Vol. 2006(2006), No. 118, pp. 1-20.

Dirichlet forms for general Wentzell boundary conditions, analytic semigroups, and cosine operator functions

Delio Mugnolo, Silvia Romanelli

Abstract:
The aim of this paper is to study uniformly elliptic operators with general Wentzell boundary conditions in suitable $L^p$-spaces by using the approach of sesquilinear forms. We use different tools to re-prove analiticity and related results concerning the semigroups generated by the above operators. In addition, we make some complementary observations on, among other things, compactness issues and characterization of domains.

Submitted June 8, 2006. Published September 28, 2006.
Math Subject Classifications: 47D06, 35J20, 35J25.
Key Words: General Wentzell boundary conditions; Dirichlet forms; Ultracontractive semigroups; Cosine operator functions.

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Delio Mugnolo
Dipartimento di Matematica
Università degli Studi di Bari
Via Orabona 4, I-70125 Bari, Italy
email: mugnolo@dm.uniba.it
Silvia Romanelli
Dipartimento di Matematica
Università degli Studi di Bari
Via Orabona 4, I-70125 Bari, Italy
email: romans@dm.uniba.it

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