Singularly perturbed equations of degenerate type
Damião J. Araújo
UNILAB/University of Florida, Department of Mathematics, Gainesville, FL 32611-7320, USAGleydson C. Ricarte
Universidade Federal Ceará, Department of Mathematics, Fortaleza, CE 60455-760, BrazilEduardo V. Teixeira
Universidade Federal Ceará, Department of Mathematics, Fortaleza, CE 60455-760, Brazil
Abstract
This work is devoted to the study of nonvariational, singularly perturbed elliptic equations of degenerate type. The governing operator is anisotropic and ellipticity degenerates along the set of critical points. The singular behavior is of order along ϵ-level layers , and a non-homogeneous source acts in the noncoincidence region . We obtain the precise geometric behavior of solutions near ϵ-level surfaces, by means of optimal regularity and sharp geometric nondegeneracy. We further investigate Hausdorff measure properties of ϵ-level surfaces. The analysis of the asymptotic limits as the ϵ parameter goes to zero is also carried out. The results obtained are new even if restricted to the uniformly elliptic, isotropic setting.
Cite this article
Damião J. Araújo, Gleydson C. Ricarte, Eduardo V. Teixeira, Singularly perturbed equations of degenerate type. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, pp. 655–678
DOI 10.1016/J.ANIHPC.2016.03.004