Regularity properties for quasiminimizers of a (p, q)-Dirichlet integral

Antonella Nastasi*, Cintia Pacchiano Camacho

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

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 Poincaré inequality. For the interior regularity, we use De Giorgi type conditions to show that quasiminimizers are locally Hölder 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 Hölder 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.

Original languageEnglish
Article number227
Number of pages37
JournalCalculus of Variations and Partial Differential Equations
Volume60
Issue number6
DOIs
Publication statusPublished - Dec 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • (p, q)-Laplace operator
  • Measure metric spaces
  • Minimal p-weak upper gradient
  • Minimizer

Fingerprint

Dive into the research topics of 'Regularity properties for quasiminimizers of a (p, q)-Dirichlet integral'. Together they form a unique fingerprint.

Cite this