Second Order Elliptic Equations in $\mathbb{R}^{d} $ with Piecewise Continuous Coefficients

Abstract

The existence and uniqueness of solutions of second order elliptic differential equations in \(\mathbb{R}^{d} \) are proved. The coefficients of second order terms are allowed to have discontinuity at finitely many parallel hyper-planes in \(\mathbb{R}^{d} \) and the first derivatives of solutions can have jumps at the hyper-planes.