0000000001237155

AUTHOR

Cintia Pacchiano Camacho

showing 2 related works from this author

Higher integrability and stability of (p,q)-quasiminimizers

2023

Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a $(p,q)$-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents $p$ and $q$. The setting is a doubling metric measure space supporting a Poincar\'e inequality.

Mathematics - Analysis of PDEsApplied MathematicsFOS: Mathematics31E05 30L99 46E35AnalysisAnalysis of PDEs (math.AP)(pq)-Laplace operator Measure metric spaces Minimal p-weak upper gradient Minimizer
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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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