Abstract
Let Lu= - Σi,j=1N aij(x, u)D ijU. Consider the quasilinear elliptic equation Lu + f(x,u,Δu) = 0 on a bounded smooth domain Ω, in ℝN. It is shown that if the oscillation of aij(x,r) with respect to r is sufficiently small and f(x,r, ξ) has a sub-linear growth in r and ξ, then there exists a solution u ∈ W2,p(Ω) ∩ W0 1,p(Ω). The existence of W2,p(Ω) ∩ W 01,p(Ω) solutions to the equation Lu + c(x, u)u + f(x, u, ∇u) = 0, where β ≥ c(x, r) ≥ α > 0, remains valid if f has a sub-quadratic growth in ξ.
Original language | English |
---|---|
Pages (from-to) | 9-15 |
Number of pages | 7 |
Journal | International Journal of Pure and Applied Mathematics |
Volume | 55 |
Issue number | 1 |
State | Published - 2009 |
Keywords
- Quasilinear elliptic equation W-estimate W (Ω)∩W(Ω)Solution