与双调和方程相关的连续模和Heinz-Schwarz型不等式
Modulus of Continuity and Heinz-Schwarz Type Inequalities of Solutions to Biharmonic Equations
对于给定的两个正整数n ≥ 2和m ≥ 1,假设函数f满足如下条件:(1)在Bn内满足非齐次双调和方程△(△f)=g(g ∈ C(Bn,Rm));(2)在Sn-1上满足f=ψ1(ψ1 ∈ C(Sn-1,Rm)),以及∂f/∂n=ψ2(ψ2 ∈ C(Sn-1,Rm)),其中∂/∂n表示内法线方向导数,Bn表示Rn中的单位球以及Sn-1表示Bn的边界.本文主要研究f的连续模和Heinz-Schwarz型不等式.
For positive integers n ≥ 2 and m ≥ 1, consider a function f satisfying the following: (1) the inhomogeneous biharmonic equation △(△f) = g (g ∈ C (Bn, Rm)) in Bn; (2) the boundary conditions f= ψ1 (ψ1 ∈ C (Sn-1, Rm)) on Sn-1 and ∂f/∂n = ψ2 (ψ2 ∈ C (Sn-1, Rm)) on Sn-1, where ∂/∂n stands for the inward normal derivative, Bn is the unit ball in Rn and Sn-1 is the unit sphere of Bn. The main aim of this paper is to discuss the Heinz–Schwarz type inequalities and the modulus of continuity of the solutions to the above inhomogeneous biharmonic Dirichlet problem.
非齐次双调和Dirichlet问题 / 连续模 / Heinz-Schwarz型不等式 {{custom_keyword}} /
inhomogeneous biharmonic Dirichlet problem / modulus of continuity / the Heinz-Schwarz type inequality {{custom_keyword}} /
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