Regularity properties for quasiminimizers of a $(p,q)$-Dirichlet integral
| Autor: | Cintia Pacchiano Camacho, Antonella Nastasi |
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| Přispěvatelé: | Nastasi, A, Camacho, CP |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pointwise
Applied Mathematics Mathematical analysis Poincaré inequality Boundary (topology) Hölder condition Metric Geometry (math.MG) Functional Analysis (math.FA) Dirichlet integral Mathematics - Functional Analysis symbols.namesake Metric space Maximum principle Mathematics - Analysis of PDEs Mathematics - Metric Geometry Settore MAT/05 - Analisi Matematica symbols FOS: Mathematics (p q)-Laplace operator Measure metric spaces Minimal p-weak upper gradient Minimizer 31E05 30L99 46E35 Analysis Harnack's inequality Mathematics Analysis of PDEs (math.AP) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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