Work

Gradient Integrability for Bounded $$\textrm{BD}$$-Minimizers

Year: 2026

Type: article

Abstract: We establish that locally bounded relaxed minimizers of degenerate elliptic symmetric gradient functionals on $$\textrm{BD}(\Omega )$$ BD ( Ω ) have weak gradients in $$\textrm{L}_{\textrm{loc}}^{1}(\Omega ;\mathbb {R}^{n\times n})$$ L loc 1 ( Ω ; R n × n ) . This is achieved for the sharp ellipticity range that is presently known to yield $$\textrm{W}_{\textrm{loc}}^{1,1}$$ W loc 1 , 1 -regularity in the full gradient case on $$\textrm{BV}(\Omega ;\mathbb {R}^{n})$$ BV ( Ω ; R n ) . As a consequence, we also obtain the first Sobolev regularity results for minimizers of the area-type functional on $$\textrm{BD}(\Omega )$$ BD ( Ω ) .

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-026-02170-y

Authors: Lisa Beck, Ferdinand Eitler, Franz Gmeineder

Institutions: University of Augsburg, University of Konstanz

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Hector Stiftung, Hector Stiftung II