A maximum principle for the system Δu − ∇W(u)=0

Panagiotis Antonopoulos; Panayotis Smyrnelis

doi:10.1016/j.crma.2016.03.015

Partial differential equations/Calculus of variations

A maximum principle for the system Δu − ∇W(u)=0

Presented by: Haïm Brézis

Panagiotis Antonopoulos ¹; Panayotis Smyrnelis ²

¹ Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece
² Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile

Comptes Rendus. Mathématique, Volume 354 (2016) no. 6, pp. 595-600.

Abstract
Résumé

A maximum principle is established for minimal solutions to the system $Δ u - \nabla W (u) = 0$ , with a potential W vanishing at the boundary of a closed convex set $C_{0} \subset R^{m}$ , which is either $C^{2}$ smooth or coincides with a point ${a}$ .

Nous établissons un principe du maximum pour les solutions minimales du système $Δ u - \nabla W (u) = 0$ , dont le potentiel W s'annule à la frontière d'un ensemble fermé convexe $C_{0} \subset R^{m}$ , de classe $C^{2}$ ou réduit à un point ${a}$ .

Received: 2015-08-05
Accepted: 2016-04-01
Published online: 2016-04-14

DOI: 10.1016/j.crma.2016.03.015

Author's affiliations:

Panagiotis Antonopoulos ¹; Panayotis Smyrnelis ²

¹ Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece
² Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile

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     author = {Panagiotis Antonopoulos and Panayotis Smyrnelis},
     title = {A maximum principle for the system {\ensuremath{\Delta}\protect\emph{u}\,\ensuremath{-}\,\ensuremath{\nabla}\protect\emph{W}(\protect\emph{u})=0}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {595--600},
     publisher = {Elsevier},
     volume = {354},
     number = {6},
     year = {2016},
     doi = {10.1016/j.crma.2016.03.015},
     language = {en},
}

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Panagiotis Antonopoulos; Panayotis Smyrnelis. A maximum principle for the system Δu − ∇W(u)=0. Comptes Rendus. Mathématique, Volume 354 (2016) no. 6, pp. 595-600. doi : 10.1016/j.crma.2016.03.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.03.015/

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