Abstract
This paper deals with a-priori estimates for Dirichlet's problem for quasilinear elliptic equations
in the plane. We give an a-priori estimate for the C2+α-norms of all solutions under the following assumptions only: The principal part is uniformly elliptic, f has quadratical growth with respect to ∇u, aij and f are Hölder-continuous and an a-priori estimate for sup|u| is known.
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VON WAHL, W.: A-priori Schranken für semilineare und quasilineare parabolische Differentialgleichungen. Math. Z., erscheint demnächst.
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von Wahl, W. Über quasilineare elliptische Differentialgleichungen in der Ebene. Manuscripta Math 8, 59–67 (1973). https://doi.org/10.1007/BF01317577
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DOI: https://doi.org/10.1007/BF01317577