A survey on anisotropic integral representation results

2025/09/15 by Verzellesi, Simone
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.11760

Abstract

In this note we review some recent results concerning integral representation properties of local functionals driven by Lipschitz continuous anisotropies.

Citations

• Variational convergences under moving anisotropies
• Variational properties of local functionals driven by arbitrary anisotropies
• The Aronsson Equation for Absolute Minimizers of Supremal Functionals in Carnot-Carathéodory Spaces
• Γ-Compactness of Some Classes of Integral Functionals Depending on Vector Fields
• Γ-convergence of nonconvex integrals in Cheeger-Sobolev spaces and homogenization
• On the relaxation of variational integrals in metric Sobolev spaces
• The Aronsson equation for absolute minimizers of L^∞-functionals associated with vector fields satisfying Hörmander's condition
• Balls and metrics defined by vector fields I: Basic properties

Related

• Variational properties of local functionals driven by arbitrary anisotropies
• Sobolev and Lipschitz regularity for local minimizers of widely\n degenerate anisotropic functionals
• Local integral transforms and global spectral decomposition
• Integral geometry of translation invariant functionals, I: The polytopal case
• Asymptotic mean value properties for fractional anisotropic operators