A.F.M. TER ELST, .; OUHABAZ, El Maati

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A.F.M. TER ELST, .
University of Auckland [Auckland]

OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

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Let Ω be a bounded domain in R d with Lipschitz boundary Γ. We define the Dirichlet-to-Neumann operator N on L 2 (Γ) associated with a second order elliptic operator A = − d k,j=1 ∂ k (c kl ∂ l) + d k=1 b k ∂ k − ∂ k (c k ·) + a 0. We prove a criterion for invariance of a closed convex set under the action of the semigroup of N. Roughly speaking, it says that if the semigroup generated by −A, endowed with Neumann boundary conditions, leaves invariant a closed convex set of L 2 (Ω), then the 'trace' of this convex set is invariant for the semigroup of N. We use this invariance to prove a criterion for the domination of semigroups of two Dirichlet-to-Neumann operators. We apply this criterion to prove the diamagnetic inequality for such operators on L 2 (Γ).< Réduire

Mots clés en anglais

Dirichlet-to-Neumann operator

invariance of convex sets

domination of semi- groups

diamagnetic inequality Home institutions:

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The diamagnetic inequality for the Dirichlet-to-Neumann operator

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Résumé en anglais

Mots clés en anglais

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