Qualitative properties of solutions to elliptic singular problems

Abstract

We investigate the singular boundary value problem in , on , where . For , we find the estimate where depends on only, denotes the distance from to and is suitable constant. For , we prove that the function is concave whenever is convex. A similar result is well known for the equation , with . For , and we prove convexity sharpness results.

Keywords

• Singular equations
• Boundary behaviour
• Convexity