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 30 Jan 2024


Published Paper

Inserted: 25 sep 2023
Last Updated: 30 jan 2024

Year: 2020

ArXiv: 2309.12736 PDF


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.