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...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. ...

* 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 ...

...perators. In fact, the extremal operators are also the maximal and minimal nonlinear uniformly elliptic operators with respect to $\mathcal L$ that vanish at ze ...first1=Luis | title=Hölder estimates for solutions of integro-differential equations like the fractional Laplace | url=http://dx.doi.org/10.1512/iumj.2006.55.27 ...

In this page we collect some results in nonlocal equations that contradict the intuition built in analogy with the local case. === Traveling fronts in Fisher-KPP equations with fractional diffusion have exponential speed === ...

...conditions. The main difference with the local case, is that for nonlocal equations the Dirichlet condition has to be taken in the whole complement of the doma === Proper elliptic equations with $x$ dependence === ...

...r in general any equation derived from jump processes will be some [[fully nonlinear integro-differential equation]]. ...tic models, in particular particle systems, can be used to derive nonlocal equations like the [[Nonlocal porous medium equation]], the [[Hamilton-Jacobi equatio ...

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 ...

...e Giorgi-Nash-Moser theorem]] or [[Krylov-Safonov theorem]]), for nonlocal equations one needs to assume that the function is nonnegative in the full space. ...ightly related to [[Holder estimates]] for solutions to elliptic/parabolic equations. For a large class of problems both statements are equivalent. But there ar ...

==Definitions: linear equations== ...s an overview of the subject and to familiarize ourselves with the type of equations under study. ...

...ant. From this monotonicity, a [[comparison principle]] can be derived for equations involving the fractional Laplacian. This formula is the most useful to study local properties of equations involving the fractional Laplacian and regularity for critical semilinear p ...

...ms for integro-differential equations with rough coefficients or nonlinear equations = == Hölder estimates for singular integro-differential equations == ...