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...ation for which the opposite happens. In order to check whether a nonlocal equations holds at a point, information about the values of the function far from tha ...ng the [[fractional Laplacian]] are the prime example of nonlocal elliptic equations. ...

...s to a variety of methods to prove existence, uniqueness or regularity for equations that are in some sense ''close'' to an equation that is well understood. If # Well posedness results for evolution equations locally in time. ...

...uation of order $\sigma$ is the name currently given to two very different equations, namely ...xtremely different behaviors. They are both fractional order [[Quasilinear equations]]. ...

<div style="top:+0.2em; font-size:95%;">This is the Nonlocal Equations Wiki</div> ...find information on a specific topic, you may want to check the [[list of equations]] or use the search option on the left. ...

* The [[Boltzmann equation]] models the evolution of dilute gases and it is intrinsically an integral equation. In fact, simp ...tic models, in particular particle systems, can be used to derive nonlocal equations like the [[Nonlocal porous medium equation]], the [[Hamilton-Jacobi equatio ...

The surface quasi-geostrophic (SQG) equation consists of an evolution equation for a scalar function $\theta: \R^+ \times \R^2 \to \R$. In the in * '''Evolution of a modulus of continuity''' <ref name="KNV"/>: An explicit modulus of con ...

* Improve the page on [[Active scalar equations]]. ...Nonlocal Phase Field Equations]] this will include many types of evolution equations such as nonlocal reaction-diffusion, models arising from nonlocal ising mod ...

...icles in a gas, but only statistically. However, this equation and related equations are used in other physical situations, such as in optics. The corresponding ...t a single equation but a family of equations, where one obtains different equations depending on the nature of the interaction between particles (see below). A ...

...between two nearby horizontal plates<ref name="MR0097227"/>. The following equations are given for a non-negative pressure $u=u(x,t)$, supported in in a time de ...

...linear term plus a lower order nonlinear term. For elliptic and parabolic equations, the two effective possibilities for the linear term is to be either the [[ ...he definition above are still considered semilinear. For example evolution equations of the form ...

A drift-(fractional)diffusion equation refers to an evolution equation of the form ...equations from fluid dynamics (for example the [[surface quasi-geostrophic equations]]). For this reason, the assumption that $\mathrm{div} \ b = 0$ is taken so ...

result. The corresponding result for elliptic equations of second order is the ...nack inequality. However, there are simple example of integro-differential equations for which the Hölder estimates hold and the Harnack inequality does not <r ...