Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations

User’s guide to viscosity solutions of second order partial differential equations

Michael G. Crandall, Hitoshi Ishii, Pierre-Louis Lions · Bulletin of the American Mathematical Society · 1992 · 4.9K citations · Full text

Numerical Analysis, Engineering, Geometric Partial Differential Equation +11

On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's

Hitoshi Ishii · Communications on Pure and Applied Mathematics · 1989 · 363 citations

Elliptic Equation, Engineering, Fluid Mechanics +9

The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations

Robert Jensen · Archive for Rational Mechanics and Analysis · 1988 · 332 citations

Engineering, Geometric Partial Differential Equation, Free Boundary Problem +7

On viscosity solutions of fully nonlinear equations with measurable ingredients

Luis Caffarelli, Michael G. Crandall, Maciej Kocan · Communications on Pure and Applied Mathematics · 1996 · 305 citations

Viscosity Solution, Monge-ampere Equation, Elliptic Equation +8

Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains

Yoshikazu Giga · EPrints - Department of Mathematics, Hokkaido University · 1991 · 202 citations

Convexity Preserving Properties, Singularly Perturbed Problem, Comparison Principle +6