Krylov and Safonov estimates for degenerate quasilinear PDEs
Event details
| Date | 18.04.2012 |
| Hour | 10:15 › 11:15 |
| Speaker | François Delarue |
| Location | |
| Category | Conferences - Seminars |
We present here a probabilistic strategy for investigating the Hölder regularity of the viscosity solutions of a degenerate quasilinear elliptic PDE of nondivergence
form. The diffusion matrix may degenerate when the norm of the gradient of the solution is small: the exhibited Hölder exponent and Hölder constant only depend on the growth of the source term and on the bounds of the spectrum of the diffusion matrix for large values of the gradient. In particular, the given estimate is independent of the regularity of the coefficients. To finish with, we will also explain conceivable strategies for an extension to the parabolic setting.
form. The diffusion matrix may degenerate when the norm of the gradient of the solution is small: the exhibited Hölder exponent and Hölder constant only depend on the growth of the source term and on the bounds of the spectrum of the diffusion matrix for large values of the gradient. In particular, the given estimate is independent of the regularity of the coefficients. To finish with, we will also explain conceivable strategies for an extension to the parabolic setting.
Practical information
- General public
- Free
Organizer
- CIB
Contact
- Isabelle Derivaz-Rabii