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Dirichlet and Neumann boundary conditions for the p-Laplace operator: what is in between?

Published online by Cambridge University Press:  20 September 2012

Ralph Chill  and
Mahamadi Warma
Ralph Chill
Affiliation:
Laboratoire de Mathématiques et Applications de Metz, Université Paul Verlaine – Metz et CNRS, Bât. A, Ile du Saulcy, 57045 Metz Cedex 1, France (chill@univ-metz.fr)
Mahamadi Warma
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, University of Puerto Rico (Rio Piedras Campus), PO Box 70377, San Juan, PR 00936-8377, USA (warma@uprrp.edu)
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Abstract

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Let p ∈ (1, ∞) and let Ω ⊆ ℝN be a bounded domain with Lipschitz continuous boundary. We characterize on L2(Ω) all order-preserving semigroups that are generated by convex, lower semicontinuous, local functionals and are sandwiched between the semigroups generated by the p-Laplace operator with Dirichlet and Neumann boundary conditions. We show that every such semigroup is generated by the p-Laplace operator with Robin-type boundary conditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 5 , October 2012 , pp. 975 - 1002
Copyright
Copyright © Royal Society of Edinburgh 2012