Boundary Regularity for Functions in De Giorgi Classes
Abstract It is well-known that functions in De Giorgi classes are continuous up to the boundary, if this satisfies a geometric density condition, and the Dirichlet boundary datum is itself continuous. We give a new proof of this classical result relying on ideas that were originally proposed by Gariepy and Ziemer to prove the sufficient part of the Wiener criterion for the continuity of solutions to quasilinear elliptic equations of p -Laplace type.
Authors
- Ugo Gianazza (ORCID: https://orcid.org/0000-0003-2558-560X)
- Zheng Li (ORCID: https://orcid.org/0000-0003-0252-6199)
Institutions
- Jilin University (CN)
- University of Pavia (IT)
Publication Details
- Journal
- La Matematica
- Published
- 2025-09-03
- DOI
- https://doi.org/10.1007/s44007-025-00174-w
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- China Scholarship Council
- Università degli Studi di Pavia
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni