| 与双调和方程相关的连续模和Heinz-Schwarz型不等式 |
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| 引用本文： | 陈少林. 与双调和方程相关的连续模和Heinz-Schwarz型不等式[J]. 数学学报, 1936, 63(5): 505-522 |
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| 作者姓名： | 陈少林 |
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| 作者单位： | 衡阳师范学院数学与统计学院 衡阳 421008 |
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| 基金项目： | 湖南省教育厅优秀青年基金项目（18B365）;湖南省科技计划项目（2016TP1020）;湖南省高等学校双一流应用特色学科"数学"（湘教通[2018]469）;衡阳市科技计划项目（2018KJ125） |
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| 摘 要： | 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.
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Modulus of Continuity and Heinz-Schwarz Type Inequalities of Solutions to Biharmonic Equations |
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| Shao Lin CHEN. Modulus of Continuity and Heinz-Schwarz Type Inequalities of Solutions to Biharmonic Equations[J]. Acta Mathematica Sinica, 1936, 63(5): 505-522 |
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| Authors: | Shao Lin CHEN |
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| Affiliation: | College of Mathematics and Statistics, Hengyang Normal University, Hengyang 421008, P. R. China |
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| Abstract: | 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. |
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| Keywords: | inhomogeneous biharmonic Dirichlet problem modulus of continuity the Heinz-Schwarz type inequality |
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