Search results for "Dirichlet integral"

showing 2 items of 2 documents

Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2

2009

AbstractWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.

General MathematicsDirichlet L-functionasymptotically linear multiplicity second order planar systems Morse indexDirichlet's energyDirichlet integralsymbols.namesakeDirichlet eigenvalueSettore MAT/05 - Analisi MatematicaDirichlet's principleOrdinary differential equationDirichlet boundary conditionsymbolsApplied mathematicsGeneral Dirichlet seriesMathematics
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Regularity properties for quasiminimizers of a $(p,q)$-Dirichlet integral

2021

Using a variational approach we study interior regularity for quasiminimizers of a $(p,q)$-Dirichlet integral, as well as regularity results up to the boundary, in the setting of a metric space equipped with a doubling measure and supporting a Poincar\'{e} inequality. For the interior regularity, we use De Giorgi type conditions to show that quasiminimizers are locally H\"{o}lder continuous and they satisfy Harnack inequality, the strong maximum principle, and Liouville's Theorem. Furthermore, we give a pointwise estimate near a boundary point, as well as a sufficient condition for H\"older continuity and a Wiener type regularity condition for continuity up to the boundary. Finally, we cons…

PointwiseApplied MathematicsMathematical analysisPoincaré inequalityBoundary (topology)Hölder conditionMetric Geometry (math.MG)Functional Analysis (math.FA)Dirichlet integralMathematics - Functional Analysissymbols.namesakeMetric spaceMaximum principleMathematics - Analysis of PDEsMathematics - Metric GeometrySettore MAT/05 - Analisi MatematicasymbolsFOS: Mathematics(p q)-Laplace operator Measure metric spaces Minimal p-weak upper gradient Minimizer31E05 30L99 46E35AnalysisHarnack's inequalityMathematicsAnalysis of PDEs (math.AP)
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