Absence of Lavrentiev's gap for anisotropic functionals

2022/10/27 by Borowski, Michał, Chlebicka, Iwona, Miasojedow, Błażej · 2 citations
#46E30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2210.15217

Abstract

We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a non-autonomous variational problem of a general structure, where the integrand is assumed to be controlled by a function which is convex and anisotropic with respect to the last variable. This fact results from new results on good approximation properties of the natural underlying unconventional function space. Scalar and vector-valued problems are studied.

Cited by

• Smoothness of weight sharply discards Lavrentiev's gap for double phase functionals
• Gradient regularity for double-phase orthotropic functionals

Related

• Discarding Lavrentiev's Gap in Non-autonomous and Non-Convex Variational Problems
• The Lavrentiev phenomenon in calculus of variations with differential forms
• Non-occurrence of gap for one-dimensional non autonomous functionals
• On global absence of Lavrentiev gap for functionals with (p,q)-growth
• Avoidance of the Lavrentiev gap for one-dimensional non autonomous functionals with state constraints