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On two-dimensional quasi-linear elliptic systems

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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.

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Dedicated to Charles B. Morrey, Jr.

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Frehse, J. On two-dimensional quasi-linear elliptic systems. Manuscripta Math 28, 21–49 (1979). https://doi.org/10.1007/BF01647963

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Keywords

  • Lower Order
  • Number Theory
  • Order Term
  • Algebraic Geometry
  • Topological Group