Search results for "p-harmonic equation"

showing 2 items of 2 documents

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
researchProduct

Radó-Kneser-Choquet Theorem for simply connected domains (p-harmonic setting)

2018

A remarkable result known as Rad´o-Kneser-Choquet theorem asserts that the harmonic extension of a homeomorphism of the boundary of a Jordan domain ⌦ ⇢ R2 onto the boundary of a convex domain Q ⇢ R2 takes ⌦ di↵eomorphically onto Q . Numerous extensions of this result for linear and nonlinear elliptic PDEs are known, but only when ⌦ is a Jordan domain or, if not, under additional assumptions on the boundary map. On the other hand, the newly developed theory of Sobolev mappings between Euclidean domains and Riemannian manifolds demands to extend this theorem to the setting on simply connected domains. This is the primary goal of our article. The class of the p -harmonic equations is wide enou…

Discrete mathematicsApplied MathematicsGeneral Mathematics010102 general mathematicsta111Semi-locally simply connectedHarmonic (mathematics)01 natural sciences010101 applied mathematicsfunktioteoriap-harmonic equationSimply connected spaceharmonic mappingsmonotone mappings0101 mathematicsCauchy's integral theoremfunktionaalianalyysiSimply connected at infinityMathematicsTransactions of the American Mathematical Society
researchProduct