Nonlinear elliptic systems with Dini continuous coefficients
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We consider nonlinear elliptic systems of divergence type with Dini continous coefficients and prove a partial regularity result for weak solutions. Our method of proof is based on a generalization of the technique of harmonic approximation. Our result is optimal in the sense that in the case of Hölder continous coefficients we establish the optimal Hölder exponent for the derivative of the weak solution on its regular set.
KeywordsWeak Solution Divergence Type Elliptic System Regularity Result Harmonic Approximation
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