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Free discontinuity problems with unbounded data: The two dimensional case

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Abstract

We prove the existence of a minimizing pair for the functionalG defined for every closed setK ⊂R 2 and for every functionu ∈C 1(ω/K) by where ω is an open set inR 2, λ, μ>0,q≥1,g ∈L q(ω) ∩L p(ω) withp>2q andH 1 is the 1-dimensional Hausdorff measure.

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  1. Dipartimento di Matematica, Università di Lecce, I-73100, Lecce, Italia

    Antonio Leaci

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  1. Antonio Leaci
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Leaci, A. Free discontinuity problems with unbounded data: The two dimensional case. Manuscripta Math 75, 429–441 (1992). https://doi.org/10.1007/BF02567096

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