On the singular set of BV minimizers for non-autonomous functionals

2024/12/19 by Lukas Fußangel, Fußangel, Lukas, Buddhika Priyasad +3
Computer Science · Mathematics · Engineering · #Optimization and Variational Analysis #Mathematical Biology Tumor Growth #Control and Stability of Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2412.14997

Abstract

We investigate regularity properties of minimizers for non-autonomous convex variational integrands F(x, D u) with linear growth, defined on bounded Lipschitz domains Ω⊂ ℝⁿ. Assuming appropriate ellipticity conditions and Hölder continuity of D_zF(x,z) with respect to the first variable, we establish higher integrability of the gradient of minimizers and provide bounds on the Hausdorff dimension of the singular set of minimizers.

Related

• Regularity for minimizers of a class of non-autonomous functionals with sub-quadratic growth
• On the regularity of minima of non-autonomous functionals
• Gradient integrability for bounded BD-minimizers
• Regularity for minimizers of non-autonomous non-quadratic functionals in the case 1 < p < 2: an a priori estimate
• Partial Regularity for Symmetric-Convex Functionals of Linear Growth