Existence Results for Boundary Problems for Uniformly Elliptic and Parabolic Fully Nonlinear Equations
Date
1999-07-01
Authors
Crandall, M. G.
Kocan, M.
Lions, P. L.
Swiech, A.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Uniformly elliptic and parabolic equations, Viscosity solutions, Good solutions, Exterior cone condition, Barrier functions
Citation
Crandall, M. G., Kocan, M., Lions, P. L., & Swiech, A. (1999). Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations. <i>Electronic Journal of Differential Equations, 1999</i>(24), pp. 1-20.
Rights
Attribution 4.0 International