A compactness result in \(GSBV^p\) and applications to \(\varGamma \)-convergence for free discontinuity problems (Q2415220)

Given the space of generalized special functions of bounded variation (GSBV), the aim is to derive compactness results without a priori bounds or fidelity terms. Applications of the compactness results are given to boundary value problems: Existence of minimizers for energy functionals under Dirichlet boundary data, and $\Gamma$-convergence of minimum values and minimizers for a sequence of boundary value problems.