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- A fully nonlinear elliptic equation is an expression of the form ...434 bytes (97 words) - 16:51, 8 April 2015
- ...-differential equations are a nonlocal version of fully nonlinear elliptic equations of the form $F(D^2 u, Du, u, x)=0$. The main examples are the integro-diffe ...nd have some [[Regularity results for fully nonlinear integro-differential equations|regularity results]]. ...8 KB (1,231 words) - 09:12, 26 June 2015
- ...iant [[fully nonlinear integro-differential equations|uniformly elliptic]] equations with respect to the [[Linear integro-differential operator|class of kernels ...t2=Luis | title=Regularity theory for fully nonlinear integro-differential equations | url=http://dx.doi.org/10.1002/cpa.20274 | doi=10.1002/cpa.20274 | year=20 ...2 KB (292 words) - 16:29, 19 May 2013
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- #REDIRECT [[Fully nonlinear integro-differential equations]] ...60 bytes (5 words) - 14:39, 27 May 2011
- #REDIRECT [[Fully nonlinear integro-differential equations]] ...60 bytes (5 words) - 11:38, 29 May 2011
- ...ome results from elliptic equations that are related to result in nonlocal equations. * [[Fully nonlinear elliptic equations]] ...345 bytes (38 words) - 13:48, 3 June 2011
- ...understood whether that such representation holds for integro-differential equations. [[Category:Fully nonlinear equations]] ...913 bytes (141 words) - 19:26, 7 February 2012
- ...iant [[fully nonlinear integro-differential equations|uniformly elliptic]] equations with respect to the [[Linear integro-differential operator|class of kernels ...t2=Luis | title=Regularity theory for fully nonlinear integro-differential equations | url=http://dx.doi.org/10.1002/cpa.20274 | doi=10.1002/cpa.20274 | year=20 ...2 KB (292 words) - 16:29, 19 May 2013
- Quasilinear equations are those which are linear in all terms except for the highest order deriv For instance, the following equations are all quasilinear (and the first two are NOT semilinear) ...980 bytes (138 words) - 21:40, 15 April 2015
- == Regularity results for linear equations with constant coefficients == == Regularity results for linear equations with smooth coefficients == ...2 KB (289 words) - 20:45, 24 April 2012
- Note that any second order fully nonlinear uniformly elliptic PDE $F(D^2 u)=0$ can be written as an Isaacs equation by A more general second order fully nonlinear uniformly elliptic PDE $F(D^2 u, Du, u, x)=0$ can also be written as an Isa ...1 KB (220 words) - 09:14, 26 June 2015
- == Linear equations == Regularity results for linear equations are applicable to nonlinear equations as well through the linearization of the equation. However, this process re ...4 KB (695 words) - 12:19, 29 January 2012
- This is a list of nonlocal equations that appear in this wiki. == Linear equations == ...3 KB (430 words) - 14:31, 15 May 2015
- ...ions. If the stochastic process is a [[Levy process]] with jumps, then the equations will have a non local part. This is a fully nonlinear convex equation. ...3 KB (523 words) - 11:00, 29 January 2012
- ...quations have $C^{2,\alpha}$ (therefore classical) solutions. This type of equations can be written as a Hamilton-Jacobi-Bellman equation. ...irst2=Luis | title=The Evans-Krylov theorem for non local fully non linear equations | year=to appear | journal=[[Annals of Mathematics]] | issn=0003-486X}}</re ...2 KB (357 words) - 19:40, 29 May 2011
- ...k solutions for elliptic or parabolic fully nonlinear integro-differential equations based on the notion of the [[comparison principle]]. It is especially suita ...finition of viscosity solutions for [[fully nonlinear integro-differential equations]] of the form $Iu=0$, assuming that the functions involved are defined in t ...2 KB (374 words) - 10:21, 25 April 2012
- One of the phenomena that are exclusive to nonlocal parabolic equations is how the boundary data, posed in the complement of a given domain might d For fully nonlinear, nonlocal parabolic equations it was established by Chang-Lara and Kriventsov<ref name="2015arXiv15050788 ...2 KB (303 words) - 11:29, 8 July 2016
- ...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. ...4 KB (619 words) - 13:34, 5 May 2014
- ...-differential equations are a nonlocal version of fully nonlinear elliptic equations of the form $F(D^2 u, Du, u, x)=0$. The main examples are the integro-diffe ...nd have some [[Regularity results for fully nonlinear integro-differential equations|regularity results]]. ...8 KB (1,231 words) - 09:12, 26 June 2015
- ...ut it also is essential in stochastic homogenization of uniformly elliptic equations in both the second order and integro-differential setting. == ABP-type estimates for integro-differential equations == ...5 KB (795 words) - 20:33, 11 March 2012
- <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. ...4 KB (596 words) - 14:09, 23 September 2013
- ...w. This makes it possible to apply to the linearization of fully nonlinear equations before knowing any a priori regularity estimate for the solution. For nonlocal equations, there are analogous results both for [[Holder estimates]] and the [[Harnac ...5 KB (882 words) - 15:31, 7 September 2012
- Given a [[fully nonlinear integro-differential equation]] $Iu=0$, [[uniformly elliptic]] with respect ...at the result is stated for general [[fully nonlinear integro-differential equations]], but the most important cases to apply it are the [[Isaacs equation]] and ...6 KB (987 words) - 13:09, 4 March 2014
- ...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. ...2 KB (351 words) - 13:17, 4 March 2014
- * 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 ...4 KB (582 words) - 16:11, 25 January 2016
- ...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 ...2 KB (374 words) - 21:43, 15 April 2015
- 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 === ...13 KB (2,026 words) - 11:37, 6 October 2015
- ...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 === ...8 KB (1,273 words) - 13:55, 31 July 2011
- ...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 ...2 KB (291 words) - 11:31, 17 November 2012
- 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 ...18 KB (2,683 words) - 10:40, 8 July 2016
- ...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 ...8 KB (1,242 words) - 10:57, 23 April 2015
- ==Definitions: linear equations== ...s an overview of the subject and to familiarize ourselves with the type of equations under study. ...96 KB (17,327 words) - 00:50, 21 June 2013
- ...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 ...12 KB (2,058 words) - 14:04, 5 August 2015
- ...ms for integro-differential equations with rough coefficients or nonlinear equations = == Hölder estimates for singular integro-differential equations == ...20 KB (3,110 words) - 09:48, 26 March 2016