Journal of Convex Analysis 33 (2026), No. 1&2, 029--055
Copyright Heldermann Verlag 2026
Characterizing BV- and BD-Ellipticity for a Class of Positively 1-Homogeneous Surface Energy Densities
Dominik Engl
Mathematisch-Geographische Fakultaet, Katholische Universitaet, Eichstaett-Ingolstadt, Germany
dominik.engl@ku.de
Carolin Kreisbeck
Mathematisch-Geographische Fakultaet, Katholische Universitaet, Eichstaett-Ingolstadt, Germany
carolin.kreisbeck@ku.de
Marco Morandotti
Dip. di Scienze Matematiche "G. L. Lagrange", Politecnico di Torino, Italy
marco.morandotti@polito.it
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.
Keywords: Interfacial energy, lower semicontinuity, BV- and BD-ellipticity, biconvexity.
MSC: 49J45; 26B25, 9Q20, 70G75.
[ Fulltext-pdf (210 KB)] open access.