# To Do List

(Difference between revisions)
 Revision as of 21:51, 12 March 2012 (view source)Luis (Talk | contribs)← Older edit Revision as of 21:53, 12 March 2012 (view source)Luis (Talk | contribs) (→(partially) Completed tasks)Newer edit → Line 51: Line 51: * Phase transitions involving non-local interactions, in particular, pages about [[Particle Systems]], discussing the Giacomin-Lebowitz theory and the Ohta-Kawasaki functional. * Phase transitions involving non-local interactions, in particular, pages about [[Particle Systems]], discussing the Giacomin-Lebowitz theory and the Ohta-Kawasaki functional. - * We may want to include a [[mini second order elliptic wiki]] inside this wiki. + * It is convenient to have 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 + * [[open problems]]. - less restrictive bound below, $C^{1,\alpha}$ estimate in bounded domains with a nonsmooth kernel, supercritical quasi-geostrophic, + - classification of nonlocal minimal cones, etc... + * Having a [[list of equations]] may make it easier to navigate the wiki. * Having a [[list of equations]] may make it easier to navigate the wiki.

## Things that need to be done

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.

• We better start thinking hard about writing the Introduction to nonlocal equations. We gotta start somewhere, so any random idea or small thing you want to write should go in there. This is high priority, since if someone reads one page of this wiki, it will likely be this one.
• Fractional curvatures in 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.
• Pages about Homogenization (local and nonlocal) should appear here too.
• Given the recent works of Osher/Gilboa and Bertozzi/Flenner on Ginzburg-Landau on graphs we should have an article on the natural similarities between non-local operators and elliptic operators on graphs.