Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372

Notice: Unexpected clearActionName after getActionName already called in /var/www/html/w/includes/Context/RequestContext.php on line 321
Optimal regularity in time and space for stochastic porous medium equations - MaRDI portal

Deprecated: Use of MediaWiki\Skin\SkinTemplate::injectLegacyMenusIntoPersonalTools was deprecated in Please make sure Skin option menus contains `user-menu` (and possibly `notifications`, `user-interface-preferences`, `user-page`) 1.46. [Called from MediaWiki\Skin\SkinTemplate::getPortletsTemplateData in /var/www/html/w/includes/Skin/SkinTemplate.php at line 691] in /var/www/html/w/includes/Debug/MWDebug.php on line 372

Deprecated: Use of MediaWiki\Skin\BaseTemplate::getPersonalTools was deprecated in 1.46 Call $this->getSkin()->getPersonalToolsForMakeListItem instead (T422975). [Called from Skins\Chameleon\Components\NavbarHorizontal\PersonalTools::getHtml in /var/www/html/w/skins/chameleon/src/Components/NavbarHorizontal/PersonalTools.php at line 66] in /var/www/html/w/includes/Debug/MWDebug.php on line 372

Deprecated: Use of QuickTemplate::(get/html/text/haveData) with parameter `personal_urls` was deprecated in MediaWiki Use content_navigation instead. [Called from MediaWiki\Skin\QuickTemplate::get in /var/www/html/w/includes/Skin/QuickTemplate.php at line 131] in /var/www/html/w/includes/Debug/MWDebug.php on line 372

Optimal regularity in time and space for stochastic porous medium equations

From MaRDI portal
(Redirected from Publication:2087392)

DOI10.1214/22-AOP1583zbMATH Open1500.35072arXiv2110.01637MaRDI QIDQ2087392

Author name not available (Why is that?)

Publication date: 27 October 2022

Published in: (Search for Journal in Brave)

Abstract: We prove optimal regularity estimates in Sobolev spaces in time and space for solutions to stochastic porous medium equations. The noise term considered here is multiplicative, white in time and coloured in space. The coefficients are assumed to be H"older continuous and the cases of smooth coefficients of at most linear growth as well as sqrtu are covered by our assumptions. The regularity obtained is consistent with the optimal regularity derived for the deterministic porous medium equation in [Gess 2020] and [Gess, Sauer, Tadmor 2020] and the presence of the temporal white noise. The proof relies on a significant adaptation of velocity averaging techniques from their usual L1 context to the natural L2 setting of the stochastic case. We introduce a new mixed kinetic/mild representation of solutions to quasilinear SPDE and use L2 based a priori bounds to treat the stochastic term.


Full work available at URL: https://arxiv.org/abs/2110.01637



zbMATH Keywords

No records found.


Mathematics Subject Classification ID

No records found.








This page was built for publication: Optimal regularity in time and space for stochastic porous medium equations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2087392)

Retrieved from "https://mardi.schubotz.org/w/index.php?title=Optimal_regularity_in_time_and_space_for_stochastic_porous_medium_equations&oldid=43523411"
Powered by MediaWiki