6533b873fe1ef96bd12d4e9d
RESEARCH PRODUCT
Regularity properties for quasiminimizers of a $(p,q)$-Dirichlet integral
Cintia Pacchiano CamachoAntonella Nastasisubject
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)description
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 consider $(p,q)$-minimizers and we give an estimate for their oscillation at boundary points.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-12-01 |