Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients.

In this paper, we prove that the weak solutions $$ u \in W^{{1,p}}_{{{\text{loc}}}} {\left( \Omega \right)}{\left( {1 < p < \infty } \right)} $$ of the following equation with vanishing mean oscillation coefficients A( x): belong to $$ W^{{1,q}}_{{{\text{loc}}}} {\left( \Omega \right)}{\left( {\forall q \in {\left( {p,\infty } \right)}} \right)} $$, provided $$ F \in L^{q}_{{{\text{loc}}}} {\left( \Omega \right)} $$ and B( x, u, h) satisfies proper growth conditions, where Ω ⊂ R N ( N ≥ 2) is a bounded open set, A( x) = ( A ij( x)) N× N is a symmetric matrix function. [ABSTRACT FROM AUTHOR]