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arXiv · 2505.00852

Superlinear free-discontinuity models: relaxation and phase-field approximation

Sergio Conti·Matteo Focardi·Flaviana Iurlano
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Abstract

In this paper we develop the Direct Method in the Calculus of Variations for free-discontinuity energies whose bulk and surface densities exhibit superlinear growth, respectively for large gradients and small jump amplitudes. A distinctive feature of this kind of models is that the functionals are defined on $SBV$ functions whose jump sets may have infinite measure. Establishing general lower semicontinuity and relaxation results in this setting requires new analytical techniques. In addition, we propose a variational approximation of certain superlinear energies via phase-field models.

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Sergio Conti, Matteo Focardi, Flaviana Iurlano. 2025-05-01. Superlinear free-discontinuity models: relaxation and phase-field approximation. https://arxiv.org/abs/2505.00852

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