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The fractional heat equation refers to the parabolic equation where $(-\Delta)^s$ stands for the [[fractional Laplacian]]. ...

...0.4171/JEMS/242 | year=2011 | journal=Journal of the European Mathematical Society (JEMS) | issn=1435-9855 | volume=13 | issue=1 | pages=1–26}} ...ultidimensional aggregation equation | doi=10.1002/cpa.20334 | year=2011 | journal=[[Communications on Pure and Applied Mathematics]] | issn=0010-3640 | volum ...

with the following properties 1) The domain $D$ is a dense subset of $L^2(\mathbb{R}^n)$ ...

...ant if under the conformal change in the metric $g_w=e^{2w}g$, the pair of the corresponding operators $A_w$ and $A$ are related by Examples of conformally invariant operators include: ...

...ntial in stochastic homogenization of uniformly elliptic equations in both the second order and integro-differential setting. == The classical Aleksandrov-Bakelman-Pucci Theorem == ...

...nonlocal equations one needs to assume that the function is nonnegative in the full space. ...ses (stable processes with the spectral measure consisting of atoms) where the Harnack inequality fails but [[Hölder estimates]] still hold true. ...

{{note|text=$1+1=2$ If I give a name or number to the parameter, math comes out just fine. ...the code itself, which after saving the page will create a placeholder for the template. ...

...in nonlocal equations that contradict the intuition built in analogy with the local case. The list should be continuously expanding. Please help by editing it. ...

Hölder continuity of the solutions can sometimes be proved only from ellipticity assumptions on the equation, without depending on smoothness of the ...

...s as an overview of the subject and to familiarize ourselves with the type of equations under study. ...the course is to see some regularity results for elliptic equations. Most of these results can be generalized to parabolic equations as well. However, t ...