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* The denoising algorithms in [[nonlocal image processing]] are able to detect patterns in a better way than the PDE based models. A simple model for denoising is the [[nonlocal mean curvature flow]].  * The denoising algorithms in [[nonlocal image processing]] are able to detect patterns in a better way than the PDE based models. A simple model for denoising is the [[nonlocal mean curvature flow]].  
* The [[Boltzmann equation]] models the evolution of dilute gases and it is intrinsically an integral equation. In fact, simplified [[kinetic models]] can be used to derive the [[fractional heat equation]] without resorting to stochastic processes.  * The [[Boltzmann equation]] models the evolution of dilute gases and it is intrinsically an integral equation. In fact, simplified [[kinetic models]] can be used to derive the [[fractional heat equation]] without resorting to stochastic processes.  
  * In conformal geometry, the Paneitz operators encode information about the manifold, they include fractional powers of the Laplacian  +  * In conformal geometry, the [[Paneitz operators]] encode information about the manifold, they include fractional powers of the Laplacian. 
* In oceanography, the temperature on the surface may diffuse though the atmosphere giving rise to the [[surface quasigeostrophic equation]].  * In oceanography, the temperature on the surface may diffuse though the atmosphere giving rise to the [[surface quasigeostrophic equation]].  
* Models for [[dislocation dynamics]] in crystals.  * Models for [[dislocation dynamics]] in crystals. 
Revision as of 18:10, 20 November 2012

We also keep a list of open problems and of upcoming events. The wiki has an assumed bias towards regularity results and consequently to equations for which some regularization occurs. But we also include some topics which are tangentially related, or even completely unrelated, to regularity. Some answers, including how to participate, can be found in the section about frequently asked questions. 

