Second order regularity for a linear elliptic system having BMO coefficients
The authors study qualitative properties of the solutions of a Dirichlet problem related to a linear elliptic system of second order. They prove that the gradient of the solution is weakly differentiable. The main assumption is that the matrix of highest order derivatives \(A(x)\) is symmetric, positive definite matrix with measurable coefficients and that the entries of the matrix \(A\) lie in the John-Nirenberg space of bounded mean oscillation class. Moreover, it is supposed a specific growth condition of the type \[ |A(x + he_i) - A(x)| \leq K(x) h, \] where \(K \in L^{n, \infty}\) plays the role of the derivative \(D_x A\).
scientific article; zbMATH DE number 7462040
scientific article