On the Lipschitz regularity of solutions of a minimum problem with free boundary

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Abstract

In this article under assumption of "small" density for negativity set, we prove local Lipschitz regularity for the one phase minimization problem with free boundary for the functional $$\mathcal E_p(v,\Omega)=\int_\Omega|\nabla v|^p+\lambda^p_1\X{u\leq0}+\lambda^p_2\X{u>0},\hspace{3mm} 1
Original languageEnglish
Pages (from-to)79-86
Number of pages8
JournalInterfaces and Free Boundaries
Volume10
Issue number1
DOIs
Publication statusPublished - 2008

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