Search results for "Variational integrals"

showing 3 items of 3 documents

Isotropic p-harmonic systems in 2D Jacobian estimates and univalent solutions

2016

The core result of this paper is an inequality (rather tricky) for the Jacobian determinant of solutions of nonlinear elliptic systems in the plane. The model case is the isotropic (rotationally invariant) p-harmonic system ...

Elliptic systemsGeneral MathematicsJacobian determinants010102 general mathematicsMathematical analysisIsotropyta111nonlinear systems of PDEsenergy-minimal deformationsDirichlet's energyp-harmonic mappingsInvariant (physics)01 natural sciencesvariational integrals010101 applied mathematicsNonlinear systemsymbols.namesakeJacobian matrix and determinantsymbolsUniqueness0101 mathematicsNonlinear elasticityMathematicsRevista Matemática Iberoamericana
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The McShane, PU and Henstock integrals of Banach valued functions

2002

Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals of vector valued functions are characterized.

McShanePettis integralPure mathematicsIntegrable systemGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsVariational integralsPU and Henstock integralPettiSettore MAT/05 - Analisi MatematicaOrdinary differential equationConvergence (routing)Vector-valued functionMultiplierMathematicsCzechoslovak Mathematical Journal
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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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