Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations

• Main Authors: M. G. Crandall, M. Kocan, P. L. Lions, A. Swiech
• Format: Article
• Language: English
• Published: Texas State University 1999-07-01
• Series: Electronic Journal of Differential Equations
• Subjects: Uniformly elliptic and parabolic equations; viscosity solutions; good solutions; exterior cone condition; barrier functions.
• Online Access: http://ejde.math.txstate.edu/Volumes/1999/24/abstr.html

We study existence of continuous weak (viscosity) solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.