An integral representation result for free-discontinuity energies defined on the space GSBVp(·) of generalized special functions of bounded variation with variable exponent is proved, under the assumption of log-Hölder continuity for the variable exponent p(x). Our analysis is based on a variable exponent version of the global method for relaxation devised in Bouchitté et al. (Arch Ration Mech Anal 165:187–242, 2002) for a constant exponent. We prove Γ -convergence of sequences of energies of the same type, we identify the limit integrands in terms of asymptotic cell formulas and prove a non-interaction property between bulk and surface contributions.
Integral representation and Γ -convergence for free-discontinuity problems with p(·) -growth
Solombrino F.
;
2023-01-01
Abstract
An integral representation result for free-discontinuity energies defined on the space GSBVp(·) of generalized special functions of bounded variation with variable exponent is proved, under the assumption of log-Hölder continuity for the variable exponent p(x). Our analysis is based on a variable exponent version of the global method for relaxation devised in Bouchitté et al. (Arch Ration Mech Anal 165:187–242, 2002) for a constant exponent. We prove Γ -convergence of sequences of energies of the same type, we identify the limit integrands in terms of asymptotic cell formulas and prove a non-interaction property between bulk and surface contributions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
