Integral Representation and T-Convergence for Free-Discontinuity Problems

Explore a 38-minute conference talk from the Workshop on "Between Regularity and Defects: Variational and Geometrical Methods in Materials Science" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into an integral representation result for free-discontinuity energies defined on the space GSBV p(.) of generalized special functions of bounded variation with variable exponent. Examine the proof under the assumption of log-Hölder continuity for the variable exponent p(x), based on a variable exponent version of the global method for relaxation. Investigate the T-convergence of sequences of energies of the same type, learn how to identify limit integrands using asymptotic cell formulas, and understand the non-interaction property between bulk and surface contributions. This talk presents joint work with G. Scilla and B. Stroffolini from the University of Naples "Federico II".