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Type: Artigo de periódico
Title: Regularity For Degenerate Two-phase Free Boundary Problems
Author: Leitao R.
de Queiroz O.S.
Teixeira E.V.
Abstract: We provide a rather complete description of the sharp regularity theory to a family of heterogeneous, two-phase free boundary problems, Jγ→min, ruled by nonlinear, p-degenerate elliptic operators. Included in such family are heterogeneous cavitation problems of Prandtl-Batchelor type, singular degenerate elliptic equations; and obstacle type systems. The Euler-Lagrange equation associated to Jγ becomes singular along the free interface {u=0}. The degree of singularity is, in turn, dimmed by the parameter γ∈[0,1]. For 0<γ<1 we show that local minima are locally of class C1,α for a sharp α that depends on dimension, p and γ. For γ=0 we obtain a quantitative, asymptotically optimal result, which assures that local minima are Log-Lipschitz continuous. The results proven in this article are new even in the classical context of linear, nondegenerate equations.
Editor: Elsevier Masson SAS
Rights: aberto
Identifier DOI: 10.1016/j.anihpc.2014.03.004
Date Issue: 2015
Appears in Collections:Unicamp - Artigos e Outros Documentos

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