Two-phase semilinear free boundary problem with a degenerate phase

Matevosyan, Norayr; Petrosyan, Arshak
July 2011
Calculus of Variations & Partial Differential Equations;Jul2011, Vol. 41 Issue 3/4, p397
Academic Journal
We study minimizers of the energy functional for $${p\in (0,1)}$$ without any sign restriction on the function u. The distinguished feature of the problem is the lack of nondegeneracy in the negative phase. The main result states that in dimension two the free boundaries $${\Gamma^+=\partial\{u>0\}\cap D}$$ and $${\Gamma^-=\partial\{u<0\}\cap D}$$ are C-regular, provided $${1-\epsilon_0


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