To Do List
Current Projects / To do list
We need to come up with some organization for the articles.
The list below can be a starting point to click on links and edit each page. The following are some of the topics that should appear in this wiki.
- Definition of viscosity solutions for nonlocal equations. Also a discussion on existence using Perron method and uniqueness through the comparison principle.
- Some discussion on Dirichlet forms, and maybe some models from nonlocal image processing.
- Some general regularity results like holder estimates, Harnack inequalities, Alexadroff-Bakelman-Pucci estimates, some reference to free boundary problems.
- A list of regularity results for fully nonlinear integro-differential equations.
- Some discussion on models involving Levy processes and stochastic control.
- Some references to equations from fluids including the surface quasi-geostrophic equation.
- A page about semilinear equations including the surface quasi-geostrophic equation and also some form of KPP.
- Nonlocal mean curvature flow (specially in connection to nonlocal image processing.
- Fractional curvatures in conformal geometry.
- We need to explain the Harmonic extension and its connection with fractional powers of the Laplacian and Conformal geometry.
- It would be wise, maybe down to the road, to add something about the Boltzmann equation, as they are some of the more "classical" and better known integro-differential equations.
We may want to include a mini second order elliptic wiki inside this wiki.
We may want to have a section on open problems, for example integral ABP for general kernels, harnack for kernels with a less restrictive bound below, C^{1,alpha} estimate in bounded domains with a nonsmooth kernel, supercritical quasi-geostrophic, classification of nonlocal minimal cones, etc...
We may want to have a list of upcoming events such as conferences, workshops, summer schools, etc.