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arXiv · 2107.12687

Relaxation of functionals with linear growth: interactions of emerging measures and free discontinuities

Stefan Krömer·Martin Kružík·Elvira Zappale
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Abstract

For an integral functional defined on functions $(u,v)\in W^{1,1}\times L^1$ featuring a prototypical strong interaction term between $u$ and $v$, we calculate its relaxation in the space of functions with bounded variations and Radon measures. Interplay between measures and discontinuities bring various additional difficulties, and concentration effects in recovery sequences play a major role for the relaxed functional even if the limit measures are absolutely continuous with respect to the Lebesgue one.

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Stefan Krömer, Martin Kružík, Elvira Zappale. 2021-07-27. Relaxation of functionals with linear growth: interactions of emerging measures and free discontinuities. https://arxiv.org/abs/2107.12687

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