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Boundary regularity for nonlinear elliptic systems

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Calculus of Variations and Partial Differential Equations Aims and scope Submit manuscript

Abstract.

We consider questions of boundary regularity for solutions of certain systems of second-order nonlinear elliptic equations. We obtain a general criterion for a weak solution to be regular in the neighbourhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighbourhood. This result is new for the situation under consideration (general nonlinear second order systems in divergence form, with inhomogeneity obeying the natural growth conditions).

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Authors and Affiliations

  1. Mathematisches Institut der Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, 91054 Erlangen, Germany (e-mail: grotow@mi.uni-erlangen.de) , , , , , , DE

    J.F. Grotowski

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  1. J.F. Grotowski
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Received: 6 July 2001 / Accepted: 27 September 2001 / Published online: 28 February 2002

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Grotowski, J. Boundary regularity for nonlinear elliptic systems. Calc Var 15, 353–388 (2002). https://doi.org/10.1007/s005260100131

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  • DOI: https://doi.org/10.1007/s005260100131

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