To Do List: Difference between revisions
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* A page about [[semilinear equations]] including the [[surface quasi-geostrophic equation]] and also some form of KPP. | * A page about [[semilinear equations]] including the [[surface quasi-geostrophic equation]] and also some form of KPP. | ||
* [[Nonlocal porous medium equation]] and its more regular sister, the [[Aggregation equation]]. | * [[Nonlocal porous medium equation]] and its more regular sister, the [[Aggregation equation]]. | ||
* [[drift-diffusion equations]]. | * [[drift-diffusion equations]]. | ||
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We may want to have a section on [[open problems]], for example integral ABP for general kernels, harnack for kernels with a | 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, | less restrictive bound below, $C^{1,alpha}$ estimate in bounded domains with a nonsmooth kernel, supercritical quasi-geostrophic, | ||
classification of nonlocal minimal cones, etc... | classification of nonlocal minimal cones, etc... | ||
*Fill up the list of [[upcoming events]] such as conferences, workshops, summer schools. | *Fill up the list of [[upcoming events]] such as conferences, workshops, summer schools. | ||
Revision as of 10:45, 2 June 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.
- 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 porous medium equation and its more regular sister, the Aggregation equation.
- Nonlocal minimal surfaces and Nonlocal mean curvature flow (specially in connection to nonlocal image processing).
- Fractional curvatures in conformal geometry.
- We need to explain further the Extension technique and its connection with fractional powers of the Laplacian and Conformal geometry.
- It would be wise (once the wiki is more mature) to add pages about the Boltzmann equation, since it is one of the more "classical" and better known integro-differential equations.
- There is also plenty of work on Dislocation dynamics that we ought to add later on.
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...
- Fill up the list of upcoming events such as conferences, workshops, summer schools.