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Optimal interior partial regularity for nonlinear elliptic systems. (English) Zbl 1191.35115

Summary: We consider interior regularity for weak solutions of nonlinear elliptic systems with subquadratic under controllable growth condition. By \(\mathcal {A}\)-harmonic approximation technique, we obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particularly, the regular result is optimal.

MSC:

35J47 Second-order elliptic systems
35J60 Nonlinear elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
35D30 Weak solutions to PDEs
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