Search results for "Degenerate elliptic equations"

showing 3 items of 3 documents

A weak comparison principle for solutions of very degenerate elliptic equations

2012

We prove a comparison principle for weak solutions of elliptic quasilinear equations in divergence form whose ellipticity constants degenerate at every point where \(\nabla u\in K\), where \(K\subset \mathbb{R }^N\) is a Borel set containing the origin.

Discrete mathematicsPure mathematicsApplied MathematicsDegenerate energy levelsWeak comparison principleMathematics::Analysis of PDEs35B51 35J70 35D30 49K20Mathematics - Analysis of PDEsSettore MAT/05 - Analisi Matematicavery degenerate elliptic equationsFOS: MathematicsPoint (geometry)Nabla symbolBorel setDivergence (statistics)Analysis of PDEs (math.AP)MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
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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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Discontinuous solutions of linear, degenerate elliptic equations

2008

Abstract We give examples of discontinuous solutions of linear, degenerate elliptic equations with divergence structure. These solve positively conjectures of De Giorgi.

Mathematics(all)Applied MathematicsGeneral MathematicsWeak solutionMathematical analysisDegenerate energy levelsStructure (category theory)Degenerate equationDegenerate elliptic equationsWeak solutionsElliptic curveDivergence (statistics)Linear equationContinuityMathematicsJournal de Mathématiques Pures et Appliquées
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