Partial Regularity for Nonlinear Elliptic Systems: The Method of A-harmonic Approximation
M. Poÿsta · 2005
We consider questions of boundary regularity for solutions of systems of second-order nonlinear elliptic equations satisfying non-homogeneous Dirichlet boundary conditions. We obtain a criterion for a weak solution to be regular in the neighbourhood of a given boundary point. The regularity proof is based on the method of so-called A-harmonic approximation. � (0), B + = B + . For x0 ∈ R n−1 × {0} we further define D�(x0) = {x = (x ' , xn) ∈ R n ; xn = 0, |x − x0| < ρ}, and set D� = D�(0), D = D1.