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)


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
$$ {\text{L(u;u) = }}{{\text{a}}_{{\text{ij}}}}{\text{(x,u,}}{{\text{u}}_{\text{x}}}{\text{)}}{{\text{u}}_{{\text{xi}}}}{{\text{x}}_{\text{j}}}{\text{ = a(x,u,}}{{\text{u}}_{\text{x}}}{\text{),}}\dag $$
in a bounded simply-connected domain Ω of two-dimensional Euclidean space E2.


Elliptic Equation Dirichlet Problem Convex Domain Piecewise Smooth Curve Convex Figure 


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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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