Abstract
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions.
| Original language | English |
|---|---|
| Pages (from-to) | 1-67 |
| Number of pages | 67 |
| Journal | Bulletin of the American Mathematical Society |
| Volume | 27 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1992 |
| Externally published | Yes |
Keywords
- Comparison theorems
- Dynamic programming
- Elliptic equations
- Fully nonlinear equations
- Generalized solutions
- Hamilton-Jacobi equations
- Maximum principles
- Nonlinear boundary value problems
- Parabolic equations
- Partial differential equations
- Perron’s method
- Viscosity solutions
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics