Asymptotic behavior of relaxed Dirichlet problems related to p-homogeneous strongly local forms

Abstract of “Asymptotic behavior of relaxed Dirichlet problems related to p-homogeneous strongly local forms” We study the asymptotic behavior of the solutions to a relaxed Dirichlet problem associated with p-homogeneous strongly local forms, $p>1$, having a local $L^1$ density and to measures $\zeta_n$, which do not charge sets of zero capacity. We prove that there exists a subsequence of $\zeta_n$ that $\gamma$-converges to a measure $\zeta$ of the same type, and we also prove the convergence of the relative solutions in $D^r [\Omega]$, $1<r<p$.