{"id":65,"date":"2021-02-08T18:50:00","date_gmt":"2021-02-08T17:50:00","guid":{"rendered":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/?p=65"},"modified":"2026-01-07T18:53:38","modified_gmt":"2026-01-07T17:53:38","slug":"log-transform-for-kinetic-fp-equations","status":"publish","type":"post","link":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/2021\/02\/08\/log-transform-for-kinetic-fp-equations\/","title":{"rendered":"Log-transform for kinetic FP equations"},"content":{"rendered":"\n<p>We just posted online with <a href=\"https:\/\/sites.google.com\/view\/guerand\/accueil\">Jessica Guerand<\/a> a new preprint entitled <em>Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations<\/em>. It is available on <a href=\"https:\/\/hal.archives-ouvertes.fr\/hal-03133950\">HAL<\/a> and on <a href=\"https:\/\/arxiv.org\/abs\/2102.04105\">arxiv<\/a>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"664\" height=\"756\" src=\"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-content\/uploads\/sites\/93\/2026\/01\/stackedcylinders.png\" alt=\"\" class=\"wp-image-15\" srcset=\"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-content\/uploads\/sites\/93\/2026\/01\/stackedcylinders.png 664w, https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-content\/uploads\/sites\/93\/2026\/01\/stackedcylinders-263x300.png 263w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\" \/><figcaption class=\"wp-element-caption\">Stacking cylinders in the proof of the weak Harnack inequality.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><strong>Abstract:<\/strong> <em>This article deals with kinetic Fokker-Planck equations with essentially bounded coefficients. A weak Harnack inequality for non-negative super-solutions is derived by considering their Log-transform and following S. N. Kruzhkov (1963). Such a result rests on a new weak Poincar\u00e9 inequality sharing similarities with the one introduced by W. Wang and L. Zhang in a series of works about ultraparabolic equations (2009, 2011, 2017). This functional inequality is combined with a classical covering argument recently adapted by L. Silvestre and the second author (2020) to kinetic equations.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We just posted online with Jessica Guerand a new preprint entitled Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations. It is available on HAL and on arxiv. Abstract: This article deals with kinetic Fokker-Planck equations with essentially bounded coefficients. A weak Harnack inequality for non-negative super-solutions is derived by considering their Log-transform and [&hellip;]<\/p>\n","protected":false},"author":138,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-65","post","type-post","status-publish","format-standard","hentry","category-preprint"],"_links":{"self":[{"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts\/65","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/users\/138"}],"replies":[{"embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/comments?post=65"}],"version-history":[{"count":3,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts\/65\/revisions"}],"predecessor-version":[{"id":67,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts\/65\/revisions\/67"}],"wp:attachment":[{"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/media?parent=65"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/categories?post=65"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/tags?post=65"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}