On BV^\mathbbA-Minimisers in two Dimensions

2025/08/14 by Ferdinand Eitler, Eitler, Ferdinand, Peter Lewintan +1
#35A15 #35B65 #35J60 #49J45 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.10508

Abstract

We investigate into the regularity of BV^\mathbbA-minimisers for ℂ-elliptic differential operators \mathbbA in 2 dimensions. Our studies strongly rely on the special structure of such differential operators. The gradient integrability is established for the sharp ellipticity range known from the (symmetric) gradient case.

Citations

• Sharp trace and Korn inequalities for differential operators
• On a class of variational problems with linear growth and radial\n symmetry
• On a Neumann problem for variational functionals of linear growth
• Sobolev regularity for Convex Functionals on BD

Related

• Gradient integrability for bounded BD-minimizers
• Partial regularity for BV^B minimizers
• Partial Regularity for \mathbbA-quasiconvex Functionals
• On the singular set of BV minimizers for non-autonomous functionals
• \mathscrA-free truncation and higher integrability of minimisers