Abstract
Abstract In this paper, we introduce the obstacle problem about the nonhomogeneous A -harmonic equation. Then, we prove the existence and uniqueness of solutions to the nonhomogeneous A -harmonic equation and the obstacle problem.
Highlights
1 Introduction In this paper, we study the nonhomogeneous A-harmonic equation
We give the definition of solutions to the nonhomogeneous A-harmonic equation and the obstacle problem
We show some properties of their solutions
Summary
We give the definition of solutions to the nonhomogeneous A-harmonic equation and the obstacle problem. −divA(x, ∇u) = f (x) is called the nonhomogeneous A-harmonic equation, where A : Rn × Rn → Rn is an operator satisfying the following assumptions for some constants 0 < a ≤ b 0, whenever ξ1, ξ2 Î Rn, ξ1 ≠ ξ2; and (V) A(x, λξ ) = λ|λ|p−2A(x, ξ ) whenever l Î R, l ≠ 0, and f is a function satisfying f Î Lp/(p-1)(Ω). A continuous solution to (2.2) in Ω is called A-harmonic function.
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