Regularity for degenerate two-phase free boundary problems
Raimundo Leitão
CMUC, Department of Mathematics, University of Coimbra, 3001-501, Coimbra, PortugalOlivaine S. de Queiroz
Departamento de Matemática, Universidade Estadual de Campinas, IMECC, Rua Sérgio Buarque de Holanda, 651, Campinas, SP, CEP 13083-859, BrazilEduardo V. Teixeira
Universidade Federal do Ceará, Campus of Pici, Bloco 914, Fortaleza, Ceará, 60455-760, Brazil
![Regularity for degenerate two-phase free boundary problems cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-aihpc-volume-32-issue-4.png&w=3840&q=90)
Abstract
We provide a rather complete description of the sharp regularity theory to a family of heterogeneous, two-phase free boundary problems, , ruled by nonlinear, -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 becomes singular along the free interface . The degree of singularity is, in turn, dimmed by the parameter . For we show that local minima are locally of class for a sharp that depends on dimension, and . For 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.
Cite this article
Raimundo Leitão, Olivaine S. de Queiroz, Eduardo V. Teixeira, Regularity for degenerate two-phase free boundary problems. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 4, pp. 741–762
DOI 10.1016/J.ANIHPC.2014.03.004