Search results for "DIRICHLET ENERGY"

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The Nitsche phenomenon for weighted Dirichlet energy

2018

Abstract The present paper arose from recent studies of energy-minimal deformations of planar domains. We are concerned with the Dirichlet energy. In general the minimal mappings need not be homeomorphisms. In fact, a part of the domain near its boundary may collapse into the boundary of the target domain. In mathematical models of nonlinear elasticity this is interpreted as interpenetration of matter. We call such occurrence the Nitsche phenomenon, after Nitsche’s remarkable conjecture (now a theorem) about existence of harmonic homeomorphisms between annuli. Indeed the round annuli proved to be perfect choices to grasp the nuances of the problem. Several papers are devoted to a study of d…

Applied MathematicsPhenomenonvariational integralharmonic mappingWeighted Dirichlet energyApplied mathematicsDirichlet's energyAnalysisMathematicsAdvances in Calculus of Variations
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Limits of Sobolev homeomorphisms

2017

Let X; Y subset of R-2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X (onto)-> Y in the Sobolev space W-1,W-p (X, R-2), p >= 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals. Peer reviewed

DIRICHLET ENERGYGeneral MathematicsDEFORMATIONSMONOTONE MAPPINGSLAPLACE EQUATION01 natural sciencesvariational integralsSobolev inequalityp-harmonic equationNONLINEAR ELASTICITYharmonic mappings111 MathematicsPOINTWISE HARDY INEQUALITIESREGULARITYSPACE0101 mathematicsMathematicsDISTORTIONSURFACESApplied Mathematics010102 general mathematicsMathematical analysisEnergy-minimal deformationsDirichlet's energy010101 applied mathematicsSobolev spaceapproximation of Sobolev homeomorphismsNonlinear elasticityJournal of the European Mathematical Society
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