Boundary behavior of large solutions to p-Laplacian elliptic equations. (February 2017) - Zhang, Zhijun
Abstract: This paper is concerned with exact asymptotic behavior near the boundary of large solutions to quasilinear elliptic equations △ p u ( x ) = b ( x ) f ( u ( x ) ), x ∈ Ω, where Ω is a bounded smooth domain in R N, △ p u = div ( | ∇ u | p − 2 ∇ u ) with p > 1, and b ∈ C ( Ω ) is nonnegative in Ω, but may be vanishing or appropriately singular (including critical singular) on the boundary. We give one new condition near infinity on f which plays a crucial role in the boundary behavior of solutions.