Nonlinear second-order elliptic equations with jump discontinuous coefficients. I: Quasilinear equations
The paper is the first in a series of two, dealing with the Dirichlet problem for quasilinear and fully nonlinear uniformly elliptic equations with coefficients with a possible jump along a surface and smooth on both sides of it. This first paper treats the quasilinear case. The authors formulate some uniqueness results (valid also for fully nonlinear equations). Then they regularize the given equation by using a suitable cut-off function and replacing the elliptic operator by the Laplacian in a neighborhood of the surface. Suitable a priori estimates and the Cantor diagonalization process provide the convergence of the classical solutions of the regularized problems to a weak solution of the original one.
scientific article; zbMATH DE number 94949