The p-Laplacian with respect to measures

TL;DR

This paper defines a p-Laplace operator for positive finite Borel measures under an Adams-type embedding condition, extending classical differential operators to a measure-theoretic setting.

Contribution

It introduces a novel measure-based p-Laplace operator applicable to measures satisfying specific embedding conditions, broadening the scope of differential operators.

Findings

Defined the p-Laplace operator for measures

Established conditions for the operator's applicability

Extended classical PDE concepts to measure spaces

Abstract

We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.