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The Dirichlet Problem for Two-Dimensional Quasi-Linear Second-Order Elliptic Equations

  • N. M. Ivochkina
Part of the Problems in Mathematical Analysis / Problemy Matematicheskogo Analiza / Πроблемы Математического Анализа book series (PMA)

Abstract

The present article is devoted to an investigation of the solubility of the Dirichlet problem in the class \( {{\text{C}}_{\text{2}}}{,_\alpha }\left( {\bar \Omega } \right)* \) for two-dimensional quasi-linear second-order elliptic equations of the form
$$ {\text{L(u;u) = }}{{\text{a}}_{{\text{ij}}}}{\text{(x,u,}}{{\text{u}}_{\text{x}}}{\text{)}}{{\text{u}}_{{\text{xi}}}}{{\text{x}}_{\text{j}}}{\text{ = a(x,u,}}{{\text{u}}_{\text{x}}}{\text{),}}\dag $$
(1)
in a bounded simply-connected domain Ω of two-dimensional Euclidean space E2.

Keywords

Elliptic Equation Dirichlet Problem Convex Domain Piecewise Smooth Curve Convex Figure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

  1. 1.
    O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasi-Linear Elliptic Equations [in Russian], Izd. “Nauka,” Moscow (1964).Google Scholar
  2. 2.
    S. N. Bernshtein, Collected Works, Vol. III (Partial Differential Equations) [in Russian], Izd. AN SSSR, Moscow (1960).Google Scholar

Copyright information

© Consultants Bureau, New York 1971

Authors and Affiliations

  • N. M. Ivochkina

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