Search results for "functions of bounded variation"

showing 5 items of 5 documents

Bounded solutions to the 1-Laplacian equation with a critical gradient term

2012

General MathematicsBounded functionMathematical analysisLaplace operator1-laplacian; degenerate elliptic equations; functions of bounded variations; gradient term with natural growthMathematicsTerm (time)Asymptotic Analysis
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Dimensional reduction for energies with linear growth involving the bending moment

2008

A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.

Mathematics(all)Asymptotic analysis49J45 49Q20 74K35dimension reductionGeneral Mathematics01 natural sciencesMathematics - Analysis of PDEsTangent measures; bending moments; dimension reductionFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsScalingFunctions of bounded variationMathematicsDeformation (mechanics)Applied Mathematics010102 general mathematicsMathematical analysisTangent measures010101 applied mathematicsNonlinear systemΓ-convergenceDimensional reductionBounded variationBending momentbending momentsVector fieldMSC: 49J45; 49Q20; 74K35Analysis of PDEs (math.AP)
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The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces

2010

Abstract We study the existence of a set with minimal perimeter that separates two disjoint sets in a metric measure space equipped with a doubling measure and supporting a Poincare inequality. A measure constructed by De Giorgi is used to state a relaxed problem, whose solution coincides with the solution to the original problem for measure theoretically thick sets. Moreover, we study properties of the De Giorgi measure on metric measure spaces and show that it is comparable to the Hausdorff measure of codimension one. We also explore the relationship between the De Giorgi measure and the variational capacity of order one. The theory of functions of bounded variation on metric spaces is us…

Pure mathematicsMathematics(all)General MathematicsApplied Mathematics010102 general mathematicsMathematical analysisBoxing inequalityCaccioppoli setDiscrete measureσ-finite measure01 natural sciencesRelaxed problemCapacitiesTransverse measure0103 physical sciencesComplex measureOuter measureHausdorff measure010307 mathematical physics0101 mathematicsBorel measureFunctions of bounded variationMathematicsJournal de Mathématiques Pures et Appliquées
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Relaxation of certain integral functionals depending on strain and chemical composition

2012

We provide a relaxation result in $BV \times L^q$, $1\leq q < +\infty$ as a first step towards the analysis of thermochemical equilibria.

RelaxationStrain (chemistry)Applied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysisThermodynamics02 engineering and technologyRelaxation; functions of bounded variation; quasiconvexity.01 natural sciencesquasiconvexityMathematics - Analysis of PDEsfunctions of bounded variation0202 electrical engineering electronic engineering information engineeringFOS: MathematicsRelaxation (physics)020201 artificial intelligence & image processing0101 mathematicsPhysics::Chemical PhysicsChemical compositionMathematicsAnalysis of PDEs (math.AP)
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Dimension reduction for $-Delta_1$

2012

A 3D-2D dimension reduction for $-\Delta_1$ is obtained. A power law approximation from $-\Delta_p$ as $p \to 1$ in terms of $\Gamma$- convergence, duality and asymptotics for least gradient functions has also been provided.

dimension reduction; gamma convergence; duality; functions of bounded variation; 1-laplacianMathematics - Analysis of PDEsdimension reductionfunctions of bounded variationdualitygamma convergence1-laplacian
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