Calculus of Variations and Geometric Measure Theory

A. Nastasi

Neumann $p$-Laplacian problems with a reaction term on metric spaces

created by nastasi on 25 Sep 2023
modified on 09 Dec 2024

[BibTeX]

Published Paper

Inserted: 25 sep 2023
Last Updated: 9 dec 2024

Journal: RICERCHE DI MATEMATICA
Year: 2020

ArXiv: 2309.12736 PDF

Abstract:

We use a variational approach to study existence and regularity of solutions for a Neumann $p$-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Trace theorems for functions with bounded variation are applied in the definition of the variational functional and minimizers are shown to satisfy De Giorgi type conditions.