Calculus of Variations and Geometric Measure Theory

D. Engl - C. Kreisbeck - M. Morandotti

Characterizing BV- and BD-ellipticity for a class of positively 1-homogeneous surface energy densities

created by morandott on 26 Feb 2024


Submitted Paper

Inserted: 26 feb 2024
Last Updated: 26 feb 2024

Year: 2024

ArXiv: 2402.15450 PDF


Lower semicontinuity of surface energies in integral form is known to be equivalent to BV-ellipticity of the surface density. In this paper, we prove that BV-ellipticity coincides with the simpler notion of biconvexity for a class of densities that depend only on the jump height and jump normal, and are positively 1-homogeneous in the first argument. The second main result is the analogous statement in the setting of bounded deformations, where we show that BD-ellipticity reduces to symmetric biconvexity. Our techniques are primarily inspired by constructions from the analysis of structured deformations and the general theory of free discontinuity problems.