Nondivergence elliptic equations with unbounded coefficients
Luigi Greco, Gioconda Moscariello, Teresa Radice · Discrete and Continuous Dynamical Systems - B · 2008
We study the nonvariational equation$\sum_{i,j=1}^n a_{ij}(x)\,\frac{\partial^2 u}{\partial x_i\,\partial x_j}=f$in domains of $r^n$. We assume that the coefficients $a_{ij}$ are in $BMO$ and the equation is elliptic, but not uniformly, and consider $f$ in $L^2(r^n)$, or even in the Zygmund class $L^2\log^\alpha L(r^n)$. We also solve Dirichlet problem.