Abstract
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.
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Beck, L. Partial regularity for weak solutions of nonlinear elliptic systems: the subquadratic case. manuscripta math. 123, 453–491 (2007). https://doi.org/10.1007/s00229-007-0100-8
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DOI: https://doi.org/10.1007/s00229-007-0100-8