Optimal Partial Regularity for Quasilinear Elliptic Systems with Vmo Coefficients Based on A-harmonic Approximations

@inproceedings{Zheng2015OptimalPR,
  title={Optimal Partial Regularity for Quasilinear Elliptic Systems with Vmo Coefficients Based on A-harmonic Approximations},
  author={Shenzhou Zheng},
  year={2015}
}
− Dα(A i j (x, u)Dβu j) = Bi(x, u,Du), a. e. x ∈ Ω, i = 1, 2, . . . ,N; (1.1) where A(x, u) = (A i j (x, u)) is a VMO function in x ∈ Ω uniformly with respect to u ∈ RN and continuous in u uniformly with respect to x ∈ Ω, and Bi(x, u,Du) satisfies the controllable growth. In the context, we adopt Einstein’s convention by summing over repeated indices with α, β = 1, 2, . . . , n and i, j = 1, 2, . . . ,N. Therefore, a vectorialvalued function u ∈ W loc (Ω,RN) is understood as a weak solution of… CONTINUE READING

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