To Do List and Template:Documentation/end box: Difference between pages

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imported>RayAYang
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== Things that need to be done ==
<noinclude><div></noinclude><div style="clear: both;"></div><!--So right or left floating items don't stick out of the doc box.-->
</div><!--End of green doc box--><!--
  Link box below for the doc meta-data:
-->{{#if:
  <!--Check if we should show the link box-->
  {{#ifeq: {{{link box|}}} | off
  |
  | {{{doc exist|yes}}}{{
    #switch: {{SUBJECTSPACE}}
    | {{ns:User}}
    | {{ns:Template}} = yes
    }}
  }}


We need to come up with some organization for the articles.
| {{fmbox
  | id = documentation-meta-data
  | image = none
  | style = background-color: #ecfcf4;
  | textstyle = font-style: italic;
  | text =
    {{#if: {{{link box|}}}
    | {{{link box}}}  <!--Use custom link box content-->
    | {{#if: {{{doc exist|yes}}}
      | <!--/doc exists, link to it-->
        The above [[Wikipedia:Template documentation|documentation]] is [[Wikipedia:Transclusion|transcluded]] from [[{{{docpage|{{FULLPAGENAME}}/doc}}}]]. <small style="font-style: normal">([{{fullurl:{{{docpage|{{FULLPAGENAME}}/doc}}}|action=edit}} edit] &#124; [{{fullurl:{{{docpage|{{FULLPAGENAME}}/doc}}}|action=history}} history])</small> <br>
      }}<!--
        Add links to /sandbox and /testcases when appropriate:
  -->{{#switch: {{SUBJECTSPACE}}
      | {{ns:User}}
      | {{ns:Template}} =
        Editors can experiment in this template's {{
        #ifexist: {{{sandbox| {{FULLPAGENAME}}/sandbox }}}
        | [[{{{sandbox| {{FULLPAGENAME}}/sandbox }}}|sandbox]] <small style="font-style: normal">([{{fullurl: {{{sandbox| {{FULLPAGENAME}}/sandbox }}} | action=edit }} edit] {{!}} [{{fullurl:Special:ComparePages | page1={{urlencode:{{{template page|{{FULLPAGENAME}}}}}}}&page2={{urlencode:{{{sandbox|{{FULLPAGENAME}}/sandbox}}}}}}} diff])</small>
        | sandbox <small style="font-style: normal">([{{fullurl: {{{sandbox| {{FULLPAGENAME}}/sandbox }}} | action=edit&preload=Template:Documentation/preload-sandbox }} create])</small>
        }} and {{
        #ifexist: {{{testcases| {{FULLPAGENAME}}/testcases }}}
        | [[{{{testcases| {{FULLPAGENAME}}/testcases }}}|testcases]] <small style="font-style: normal">([{{fullurl: {{{testcases| {{FULLPAGENAME}}/testcases }}} | action=edit }} edit])</small>
        | testcases <small style="font-style: normal">([{{fullurl: {{{testcases| {{FULLPAGENAME}}/testcases }}} | action=edit&preload=Template:Documentation/preload-testcases }} create])</small>
        }} pages. <br>
      }}<!--
        Show the cats and interwiki text, but not
        if "content" fed or "docname fed" since then it is
        unclear where to add the cats and interwikis.
  -->{{#if: {{{content|}}} {{{docname fed|}}}
      |
      | Please add categories and interwikis to the [[{{{docpage|{{FULLPAGENAME}}/doc}}}|/doc]] subpage.
      }}<!--
        Show the "Subpages" link:
  -->{{#switch: {{SUBJECTSPACE}}
      | {{ns:File}} =  <!--Don't show it-->
      | {{ns:Template}} = &#32;[[Special:PrefixIndex/{{{template page|{{FULLPAGENAME}}}}}/|Subpages of this template]].
      | #default = &#32;[[Special:PrefixIndex/{{{template page|{{FULLPAGENAME}}}}}/|Subpages of this page]].
      }}
    }}{{#ifexist:{{FULLPAGENAME}}/Print
    |</br>A [[Help:Books/for experts#Improving the book layout|print version]] of this template exists at [[/Print]]. If you make a change to this template, please update the print version as well.[[Category:Templates with print versions]]
    }}
  }}
}}<!--End link box--><!--


The list below can be a starting point to click on links and edit each page. The following are some of the topics that should appear in this wiki.
  Detect and report strange usage:
-->{{#if:


* We better start thinking hard about writing the [[Introduction to nonlocal equations]]. We gotta start somewhere, so any random idea or small thing you want to write should go in there. This is high priority, since if someone reads one page of this wiki, it will likely be this one.
  <!--Check if {{documentation}} is transcluded
      on a /doc or /testcases page-->
  {{#switch: {{SUBPAGENAME}}
  | doc
  | testcases = strange
  }}
  <!--More checks can be added here, just return anything
      to make the surrounding if-case trigger-->


* Some discussion on [[Dirichlet form|Dirichlet forms]], and maybe some models from [[nonlocal image processing]].
| <includeonly>[[Category:Wikipedia pages with strange ((documentation)) usage|{{main other|Main:}}{{FULLPAGENAME}}]]<!-- Sort on namespace --></includeonly>


* Fractional curvatures in conformal geometry.
}}<noinclude>
 
{{pp-template|small=yes}}
* We need  to explain further the  [[Extension technique]] and its connection with fractional powers of the Laplacian and Conformal geometry. Required background: [[Geometric Scattering Theory]], [[Ambient Metric Construction]], [[GJMS Operators]] and [[Singular Yamabe Problem]]..)
</noinclude>
 
* It would be wise (once the wiki is more mature) to add pages about the [[Boltzmann equation]], since it is one of the more "classical" and better known integro-differential equations.
 
* Pages about [[Homogenization]] (local and nonlocal) should appear here too. (CITATIONS still needed)
 
* Given the recent works of Osher/Gilboa and Bertozzi/Flenner on Ginzburg-Landau  on graphs we should have an article on the natural similarities between non-local operators and [[elliptic operators on graphs]].
 
* [[nonlocal image processing]].
 
* [[Aggregation equation]].
 
* [[Keller-Segel equation]].
 
* [[Active scalar equations]].
 
* [[Ising Models With Nonlocal Interactions]]
 
* [[Nonlocal Interaction Energies]]
 
* [[Nonlocal Phase Field Equations]] this will include many types of evolution equations such as nonlocal reaction-diffusion, models arising from nonlocal ising models, nonlocal cahn-hilliard, nonlocal biological aggregation, sharp interface limits (giacomin-lebowitz, bates-et-al, de massi-pressutti, etc...)
 
* [[Boundary Harnack Inequality]] it would be good to possibly include this in the description of what is different/same regarding local vs. nonlocal equations.
 
* describe, with references, the connection between [[holder estimates]] of viscosity solutions of stationary and or parabolic equations and the existence and uniqueness of solutions to the relevant [[Martingale Problem]]
 
*[[Neumann Boundary Conditions]]
 
*jump processes via [[Subordination]]
 
*processes in the "limit" $\alpha=0$, [[Zero Order Operators]]
 
== (partially) Completed tasks ==
 
* A sort of [[Starting page]] that serves as a "root" for all pages we add (ideally, any page we create should be reachable from here). (UPDATE: See discussion.)
 
* Definition of [[viscosity solutions]] for nonlocal equations. Also a discussion on existence using [[Perron's method]] and uniqueness through the [[comparison principle]].
 
* Some general regularity results like [[holder estimates]], [[Harnack inequalities]], [[Alexadroff-Bakelman-Pucci estimates]], some reference to [[free boundary problems]].
 
* A list of [[regularity results for fully nonlinear integro-differential equations|regularity results]] for [[fully nonlinear integro-differential equations]].
 
* Some discussion on models involving [[Levy processes]] and [[stochastic control]].
 
* The [[surface quasi-geostrophic equation]].
 
* A page about [[semilinear equations]].
 
* [[Nonlocal porous medium equation]].
 
* [[drift-diffusion equations]].
 
* [[Nonlocal minimal surfaces]] and [[Nonlocal mean curvature flow]].
 
* There is also plenty of work on [[Dislocation dynamics]] that we ought to add later on.
 
* Phase transitions involving non-local interactions, in particular, pages about [[Particle Systems]], discussing the Giacomin-Lebowitz theory and the Ohta-Kawasaki functional.
 
* It is convenient to have a [[mini second order elliptic wiki]] inside this wiki.
 
* [[open problems]].
 
* Having a [[list of equations]] may make it easier to navigate the wiki.
 
== Other ideas ==
 
 
* Fill up the list of [[upcoming events]] such as conferences, workshops, summer schools.
 
* [[User:Nestor|Nestor]] has started a [[Literature on Nonlocal Equations]] to dump there all papers we want to reference or are already referencing on the wiki.

Latest revision as of 21:33, 9 May 2011

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