Interior second derivative estimates for nonlinear diffusions

Gregoire Loeper; Fernando Quiros

Interior second derivative estimates for nonlinear diffusions

Analysis of PDEs 2019-01-01 v1

Authors: Gregoire Loeper , Fernando Quiros

Abstract

By an extension of of some estimates due to Crandall and Pierre and Di Benedetto we derive consequences for fully nonlinear parabolic equations of the form $\dt v + F(t,x,D^2v)=0$ , where $F$ can be both singular and degenerate elliptic and also non-homogeneous. Such equations appear in the theory of option pricing with market impact.

Keywords

parabolic partial differential equations nonlinear diffusion equations gradient estimates

Cite

@article{arxiv.1812.11253,
  title  = {Interior second derivative estimates for nonlinear diffusions},
  author = {Gregoire Loeper and Fernando Quiros},
  journal= {arXiv preprint arXiv:1812.11253},
  year   = {2019}
}

Related papers

View all related →