Local behaviour of singular solutions for nonlinear elliptic equations in divergence form

B. Brandolini, F. Chiacchio, F. C. Cîrstea, C. Trombetti

Abstract

We study the behaviour of all positive solutions near an isolated singularity for a class of nonlinear elliptic equations in divergence form, which can be singular or degenerate. We completely solve both questions of removability of singularities and classification of singular solutions under optimal conditions. We also obtain the existence of positive solutions in all categories of such a classification. As a main feature, our approach is developed based on regular variation theory.

Keywords: Nonlinear elliptic equations, isolated singularities, removable singularities, regular variation theory.

AMS Subject Classification: Primary 35J60; secondary 35B40, 35J25.