Calculus of Variations and Geometric Measure Theory

C. Leone - G. Scilla - F. Solombrino - A. Verde

Strong existence for free-discontinuity problems with non-standard growth

created by scilla on 10 May 2024



Inserted: 10 may 2024
Last Updated: 10 may 2024

Year: 2024


An Ahlfors-type regularity result for free-discontinuity energies defined on the space $SBV^{\varphi}$ of special functions of bounded variation with $\varphi$-growth, where $\varphi$ is a generalized Orlicz function, is proved. Our analysis expands on the regularity theory for minimizers of a class of free-discontinuity problems in the non-standard growth case.

Keywords: Free-discontinuity problems, regularity, Minimizers, non-standard growth, generalized Orlicz function