Work

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

Year: 2025

Type: article

Abstract: We investigate regularity properties of minimizers for non-autonomous convex variational integrands [Formula: see text] with linear growth, defined on bounded Lipschitz domains [Formula: see text]. Assuming appropriate ellipticity conditions and Hölder continuity of [Formula: see text] 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.

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199725500944

Authors: Lukas Fußangel, Buddhika Priyasad, Paul Stephan

Institution: University of Konstanz

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Studienstiftung des Deutschen Volkes, Universität Konstanz, Hector Stiftung

Award: G115475311