$\Gamma$-Compactness of Some Classes of Integral Functionals Depending on Vector Fields

TL;DR

This paper establishes $ ext{Gamma}$-compactness results for classes of integral functionals depending on Lipschitz vector fields, with respect to strong $L^p$ and $W_X^{1,p}$ topologies, advancing the understanding of variational convergence.

Contribution

It provides new $ ext{Gamma}$-compactness results for integral functionals depending on Lipschitz vector fields in specific topologies, extending previous theoretical frameworks.

Findings

$ ext{Gamma}$-compactness results established for classes of integral functionals

Results apply to functionals depending on Lipschitz vector fields

Advances the theoretical understanding of variational convergence in this context

Abstract

In this paper we achieve some $\Gamma$-compactness results for suitable classes of integral functionals depending on a given family of Lipschitz vector fields, with respect to both the strong $L^p-$topology and the strong $W_X^{1,p}-$topology.