Construction of $p$-energy measures associated with strongly local $p$-energy forms

Abstract

We construct canonical $p$-energy measures associated with strongly local $p$-energy forms without assuming self-similarity. Here, $p$-energy forms are $L^p$-analogues of Dirichlet forms, which have recently been studied mainly on fractals. Furthermore, we prove that these measures satisfy the chain and Leibniz rules, and that such "good" energy measures are unique. A key ingredient is a $p$-energy analogue of Le Jan's domination principle. Moreover, we show that the Korevaar$-$Schoen-type $p$-energy measures defined by Alonso-Ruiz and Baudoin (2025, Nonlinear Anal.) coincide with our canonical $p$-energy measures.