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The method of A-harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition. (English) Zbl 1387.35210

Summary: We consider the nonlinear elliptic systems under controllable growth condition. We use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition, and directly establishing the optimal Hölder exponent for the derivative of a weak solution.

MSC:

35J60 Nonlinear elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
49N60 Regularity of solutions in optimal control
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