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

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 Poincaré 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.

References in corpus (1)

• Traces of Newton-Sobolev, Hajlasz-Sobolev and BV functions on metric spaces

Cited by in corpus (1)

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