Abstract
We investigate various notions of subdifferentials and superdifferentials of nonconvex functions in Banach spaces. We prove stability results of these subdifferentials and superdifferentials under various kind of convergences. Our proofs rely on a recent variational principle of Deville, Godefroy and Zizler. Connections between our results, the geometry of Banach spaces and existence theorems of viscosity solutions for first and second-order Hamilton-Jacobi equations in infinite-dimensional Banach spaces will be explained.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 141-157 |
| Number of pages | 17 |
| Journal | Set-Valued and Variational Analysis |
| Volume | 2 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - Mar 1994 |
| Externally published | Yes |
Keywords
- Banach spaces
- Convex functions
- Mathematics Subject Classifications (1991): 49J45, 49J52
- subdifferentials
- superdifferentials
- viscosity solutions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics