Partial Regularity for BV Minimizers

Abstract

We establish an $\epsilon$-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.

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Cited by in corpus (9)

• Regularity for double phase problems at nearly linear growth
• Regularity for multi-phase problems at nearly linear growth
• Partial regularity for local minimizers of variational integrals with lower order terms
• Regularity for higher order quasiconvex problems with linear growth from below
• On the singular set of $\mathrm{BV}$ minimizers for non-autonomous functionals
• Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth
• Regularity for the Dirichlet problem on BD
• Partial regularity for variational integrals with Morrey-Hölder zero-order terms, and the limit exponent in Massari's regularity theorem
• Monotone approximation of differentiable convex functions with applications to general minimization problems