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manuscripta mathematica

, Volume 28, Issue 1–3, pp 21–49 | Cite as

On two-dimensional quasi-linear elliptic systems

  • Jens Frehse
Article

Abstract

The author shows the existence of a Hölder continuous solution for a class of two-dimensional non-linear elliptic systems of the type
$$ - \Sigma _{i = 1}^2 \partial _i a_i (x,u,\triangledown u) + a_o (x,u,\triangledown u) = 0.$$
The principal part of the equation is required to satisfy a condition of uniform ellipticity and need not be in diagonal form. The lower order term ao has at most quadratic growth in ∇u and satisfies a one-sided condition ao(x,u,βu) u≥−K or appropriate generalizations.

Keywords

Lower Order Number Theory Order Term Algebraic Geometry Topological Group 
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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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Jens Frehse
    • 1
  1. 1.Institut für Angewandte Mathematik der UniversitätBonnW-Germany

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