An Interior Regularity Property for the Solution to a Linear Elliptic System with Singular Coefficients in the Lower-Order Term

This paper deals with the interior higher differentiability of the solution u to the Dirichlet problem related to system $ -\textrm{div} (A(x) Du) + B(x,u)=f$ on a bounded lipschitz domain $\Omega$ in $\mathbb R^n$. The matrix $A(x)$ lies in the John and Nirenberg space $BMO$. The lower order term $B(x,u)$ is controlled with respect to spatial variable by a function $b(x)$ belonging to the Marcinkiewicz space $L^{n, \infty}$. The novelty here is the presence of a singular coefficient in the lower order term.