Partial Regularity for BV Minimizers

TL;DR

This paper proves a partial regularity result for BV minimizers of strongly quasiconvex variational integrals with linear growth, extending regularity theory from Sobolev spaces to BV maps and surpassing previous convexity restrictions.

Contribution

It establishes an $ ext{ extonehalf}$-regularity result for BV minimizers of strongly quasiconvex integrals, broadening the scope of regularity theory beyond convex cases.

Findings

Proves partial regularity for BV minimizers of strongly quasiconvex integrals.

Extends regularity results from Sobolev spaces to BV maps.

Generalizes previous results limited to convex integrals.

Abstract

We establish an $\varepsilon$-regularity result for the derivative of a map of bounded variation that minimizes a strongly quasiconvex variational integral of linear growth, and, as a consequence, the partial regularity of such BV minimizers. This result extends the regularity theory for minimizers of quasiconvex integrals on Sobolev spaces to the context of maps of bounded variation. Previous partial regularity results for BV minimizers in the linear growth set-up were confined to the convex situation.