A priori estimates and existence for quasi-linear elliptic equations

Academic Article

Abstract

  • We study the boundary value problem of quasi-linear elliptic equation div(|∇u|m-2∇u) + B(z,|u, ∇u) = 0 inΩ, u = 0 on ∂Ω where Ω ⊂ ℝn (n ≥ 2) is a connected smooth domain, and the exponent m ∈ (1,n) is a positive number. Under appropriate conditions on the function B, a variety of results on a priori estimates, existence and non-existence of positive solutions have been established. The results are generically optimum for the canonical prototype B = |u|p-1 u, p > m - 1. © 2008 Springer-Verlag.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Zou HH
  • Start Page

  • 417
  • End Page

  • 437
  • Volume

  • 33
  • Issue

  • 4