To Do List: Difference between revisions
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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. | 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]]. | * Some general regularity results like [[holder estimates]], [[Harnack inequalities]], [[Alexadroff-Bakelman-Pucci estimates]], some reference to [[free boundary problems]]. | ||
Revision as of 16:20, 18 May 2011
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.
- Some discussion on models involving Levy processes and stochastic control.
- Some references to equations from fluids including the surface quasi-geostrophic equations.
- Fractional curvatures in conformal geometry.
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...