The Existence of Solutions to the Dirichlet Problem for a Class of-Two Variables and Second-order Quasilinear Elliptic Equations

Wang Feng; Chen Lei

doi:10.3969/j.issn.1007-7162.2015.02.017

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The Existence of Solutions to the Dirichlet Problem for a Class of-Two Variables and Second-order Quasilinear Elliptic Equations

更新时间：2026-05-27

- The Existence of Solutions to the Dirichlet Problem for a Class of-Two Variables and Second-order Quasilinear Elliptic Equations
- Vol. 32, Issue 2, Pages: 91-97(2015)
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- DOI：10.3969/j.issn.1007-7162.2015.02.017
  CLC：
- Online First：30 May 2015，
  
  Published：2015
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汪锋, 陈磊. 一类两个变量的二阶拟线性椭圆型方程Dirichlet问题解的存在性[J]. 广东工业大学学报, 2015, 32(2): 91-97.

Wang Feng, Chen Lei. The Existence of Solutions to the Dirichlet Problem for a Class of-Two Variables and Second-order Quasilinear Elliptic Equations[J]. 2015, 32(2): 91-97.
汪锋, 陈磊. 一类两个变量的二阶拟线性椭圆型方程Dirichlet问题解的存在性[J]. 广东工业大学学报, 2015, 32(2): 91-97. DOI： 10.3969/j.issn.1007-7162.2015.02.017.

Wang Feng, Chen Lei. The Existence of Solutions to the Dirichlet Problem for a Class of-Two Variables and Second-order Quasilinear Elliptic Equations[J]. 2015, 32(2): 91-97. DOI： 10.3969/j.issn.1007-7162.2015.02.017.

摘要

拟共形映射理论是Riemann共形映射的推广，自Ahlfors等人发展半个多世纪以来，在数学的许多领域得到了广泛的应用.本文讨论一类拟线性椭圆方程Dirichlet问题的可解性，主要借助拟共形映射、Schauder内估计、闸函数及Schauder不动点定理给出一个相应的结果，这里的特殊之处是本文的讨论完全建立在两个变量的线性椭圆方程的有效的先验估计之上.

Abstract

The theory of quasiconformal mappings is the extension of Riemann conformal mappings. It has been widely applied in many mathematic fields since proposed by Ahlfors etal. This paper explores the solvability of a class of quasilinear elliptic equation Dirichlet problem by using conformal mappings

Schauder estimates

barrier function and Schauder fixed point theorem. The novelty of this paper is that our method is based on the priori estimate of linear elliptic equations of two variables.

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