The Obstacle Problem for the A-Harmonic Equation
نویسندگان
چکیده
Firstly, we define an order for differential forms. Secondly, we also define the supersolution and subsolution of the A-harmonic equation and the obstacle problems for differential forms which satisfy theA-harmonic equation, and we obtain the relations between the solutions toA-harmonic equation and the solution to the obstacle problem of the A-harmonic equation. Finally, as an application of the obstacle problem, we prove the existence and uniqueness of the solution to the A-harmonic equation on a bounded domain Ω with a smooth boundary ∂Ω, where the Aharmonic equation satisfies d A x, du 0, x ∈ Ω; u ρ, x ∈ ∂Ω, where ρ is any given differential form which belongs to W1,p Ω,Λl−1 .
منابع مشابه
The existence of solutions to the nonhomogeneous A - harmonic equation
* Correspondence: mathwy@hit. edu.cn Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China 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.
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