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arXiv · 1807.03647

A compactness result in $GSBV^p$ and applications to $\Gamma$-convergence for free discontinuity problems

Manuel Friedrich
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Abstract

We present a compactness result in the space $GSBV^p$ which extends the classical statement due to Ambrosio to problems without a priori bounds on the deformations. As an application, we revisit the $\Gamma$-convergence results for free discontinuity functionals established recently by Cagnetti, Dal Maso, Scardia, and Zeppieri. We investigate sequences of boundary value problems and show convergence of minimum values and minimizers.

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Manuel Friedrich. 2018-07-10. A compactness result in $GSBV^p$ and applications to $\Gamma$-convergence for free discontinuity problems. https://arxiv.org/abs/1807.03647

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