Partial regularity for weak solutions of nonlinear elliptic systems: the subquadratic case. (English) Zbl 1151.35023

Summary: We consider weak solutions of second order nonlinear elliptic systems of divergence type under subquadratic growth conditions. Via the method of \({\mathcal{A}}\)-harmonic approximation we give a characterization of regular points up to the boundary which extends known results from the quadratic and superquadratic case. The proof yields directly the optimal higher regularity on the regular set.


35J55 Systems of elliptic equations, boundary value problems (MSC2000)
49N60 Regularity of solutions in optimal control
35D10 Regularity of generalized solutions of PDE (MSC2000)
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