Nonlinear second-order elliptic equations with jump discontinuous coefficients. I. Quasilinear equations
Nikolai Kutev, Pierre Louis Lions · Differential and Integral Equations · 1992
This is the first paper of a series of two devoted to the study of quasilinear or fully nonlinear, second-order, uniformly elliptic equations with coefficients which are smooth on both sides of a surface without necessarily being equal on that surface.We prove that C 1 solutions exist and are unique with appropriate conditions on the nonlinearities and regularity on each side of the surface.Here, we only consider the case of quasilinear equations.The case of fully nonlinear elliptic equations will be considered in Part II.