Existence of strong solutions to some quasilinear elliptic equations

Tsang Hai Kuo*, Chu Ching Huang, Yi Jung Chen

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

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 languageEnglish
Pages (from-to)9-15
Number of pages7
JournalInternational Journal of Pure and Applied Mathematics
Volume55
Issue number1
StatePublished - 2009

Keywords

  • Quasilinear elliptic equation W-estimate W (Ω)∩W(Ω)Solution

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