REGULARITY OF WEAK SOLUTIONS TO THE MODEL VENTTSEL PROBLEM FOR LINEAR DIVERGENCE ELLIPTIC OPERATORS IN CAMPANATO SPACES

A. A. Arkhipova; A. A. Lukina

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REGULARITY OF WEAK SOLUTIONS TO THE MODEL VENTTSEL PROBLEM FOR LINEAR DIVERGENCE ELLIPTIC OPERATORS IN CAMPANATO SPACES

机译：坎帕纳托空间中线性散度椭圆算子的温特塞尔模型弱解的规律性

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We consider a linear second order divergence elliptic equation in a neighborhood of the plane part of the boundary. The boundary condition involves the second order derivatives with respect to tangent variables and the conormal derivative (a Venttsel type problem). We study the regularity of the solution and its derivatives in a neighborhood of the boundary in Campanato spaces and establish regularity in Holder spaces. The results remain valid for linear systems with strongly elliptic matrices. Bibliography: 10 titles.

机译：我们考虑边界平面部分附近的线性二阶发散椭圆方程。边界条件涉及切线变量的二阶导数和同态导数（Venttsel型问题）。我们研究了Campanato空间边界附近的解及其导数的正则性，并在Holder空间中建立了正则性。该结果对于具有强椭圆矩阵的线性系统仍然有效。参考书目：10种。

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《Journal of Mathematical Sciences》 |2013年第5期|609-621|共13页
作者
A. A. Arkhipova; A. A. Lukina;
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St. Petersburg State University 28, Universitetskii pr., Petrodvorets, St. Petersburg 198504, Russia;

St. Petersburg State University 28, Universitetskii pr., Petrodvorets, St. Petersburg 198504, Russia;

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1. PARTIAL REGULARITY OF WEAK SOLUTIONS TO THE MODEL VENTTSEL PROBLEM FOR QUASI-LINEAR ELLIPTIC SYSTEMS OF EQUATIONS. METHOD OF A-HARMONIC APPROXIMATION [J] . A. A. Arkhipova Journal of Mathematical Sciences . 2014,第6期

机译：拟线性椭圆方程组的Venttsel问题弱解的部分正则性。谐波近似的方法
2. PARTIAL REGULARITY OF SOLUTIONS TO MODEL VENTTSEL PROBLEM FOR QUASILINEAR ELLIPTIC SYSTEMS OF EQUATIONS WITH QUADRATIC NON-LINEARITY RELATIVE TO THE GRADIENT [J] . A. A. Arkhipova Journal of Mathematical Sciences . 2015,第4期

机译：具有相对于梯度的二次非线性方程组的拟线性椭圆方程组模型的Venttsel问题解的部分规则性
3. REGULARITY IN CAMPANATO SPACES FOR SOLUTIONS OF FULLY NONLINEAR ELLIPTIC SYSTEMS [J] . Luisa Fattorusso, Antonio Tarsia Discrete and continuous dynamical systems . 2011,第4期

机译：完全非线性椭圆系统解的Campanato空间中的正则性
4. The regularity estimates for the solutions of general elliptic equations in Orlicz spaces [C] . Tao Xiangxing 2011 International Conference on E-Business and E-Government . 2011

机译：Orlicz空间中一般椭圆方程解的正则估计
5. Partial regularity of weak solutions of quasilinear elliptic systems and weak Harnack inequalities. [D] . Borovikova, Marina. 2004

机译：拟线性椭圆系统的弱解的局部正则性和弱的Harnack不等式。
6. THE IDENTITY OF THE WEAK AND STRONG EXTENSIONS OF A LINEAR ELLIPTIC DIFFERENTIAL OPERATOR: II [O] . M. S. Narasimhan 1957

机译：线性椭圆型微分算子的弱扩张和强扩张的恒等式：
7. Regularity in Campanato Spaces for Solutions of Fully Nonlinear Elliptic Systems [O] . TARSIA A.A., FATTORUSSO LUISA 2011

机译：坎帕纳托空间中的规律性非线性椭圆系统的整体解
8. C(1 + Alpha) Local Regularity of Weak Solutions of Degenerate Elliptic Equations [R] . DiBenedetto, E. 1982

机译：退化椭圆型方程弱解的C（1 + alpha）局部正则性

REGULARITY OF WEAK SOLUTIONS TO THE MODEL VENTTSEL PROBLEM FOR LINEAR DIVERGENCE ELLIPTIC OPERATORS IN CAMPANATO SPACES

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