Partial regularity for BV^B minimizers

2023/10/30 by Franceschini, Federico
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.20002

Abstract

We prove an ε-regularity theorem for BV^B minimizers of strongly B-quasiconvex functionals with linear growth, where B is an elliptic operator of the first order. This generalises to the BV^B setting the analogous result for BV functions by F. Gmeineder and J. Kristensen [Arch. Rational Mech. Anal. 232 (2019)]. The results of this work cannot be directly derived from the B =∇ case essentially because of Ornstein's "non-inequality". This adaptation requires an abstract local Poincaré inequality and a fine Fubini-type property to avoid the use of trace theorems, which in general fail when B is elliptic.

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