The Moving Plane Method for Doubly Singular Elliptic Equations Involving a First-Order Term

Abstract

In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice of the cutoff functions, we deduce symmetry and monotonicity properties of the solutions.

Keywords

• semilinear elliptic equations
• singular solutions
• qualitative properties
• first-order term
• singular nonlinearity
• 35a21
• 35b06
• 35b50
• 35j61
• 35j75