Regularity for degenerate two-phase free boundary problems

Autor(es)

Leitao, Raimundo ^[1] ; de Queiroz, Olivaine S. ^[2] ; Teixeira, Eduardo V. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra - Portugal

^[2] Univ Estadual Campinas, Dept Matemat, IMECC, BR-13083859 Campinas, SP - Brazil

^[3] Univ Fed Ceara, BR-60455760 Fortaleza, Ceara - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ANNALES DE L' INSTITUT HENRI POINCARÉ-ANALYSE NON LINÉAIRE; v. 32, n. 4, p. 741-762, JUL-AUG 2015.
• Citações Web of Science: 9

Resumo

We provide a rather complete description of the sharp regularity theory to a family of heterogeneous, two-phase free boundary problems, J(gamma) -> 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 J(gamma) becomes singular along the free interface [u = 0]. The degree of singularity is, in turn, dimmed by the parameter gamma epsilon {[}0, 1]. For 0 < gamma < 1 we show that local minima are locally of class C-1,C-alpha for alpha sharp a that depends on dimension, p and gamma. For gamma = 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. (C) 2014 Elsevier Masson SAS. All rights reserved. (AU)

• Processo FAPESP: 12/20197-0 - Aspectos locais de problemas elípticos e parabólicos
• Beneficiário: Olivâine Santana de Queiroz
• Modalidade de apoio: Auxílio à Pesquisa - Regular