Kolmogorov–Fokker–Planck equations: Comparison principles near Lipschitz type boundaries

We prove several new results concerning the boundary behavior of non-negative solutions to the equation Ku=0, whereK:=∑i=1m∂xixi+∑i=1mxi∂yi−∂t. Our results are established near the non-characteristic part of the boundary of certain local LipK-domains, where the latter is a class of local Lipschitz t...

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Bibliographic Details
Published inJournal de mathématiques pures et appliquées Vol. 106; no. 1; pp. 155 - 202
Main Authors Nyström, K., Polidoro, S.
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.07.2016
Subjects
Boundary estimate
Hypoelliptic
Kolmogorov equation
Kolmogorov–Fokker–Planck equation
Matematik
Mathematics
Ultraparabolic
Ultraparabolic
35H20
Kolmogorov–Fokker–Planck equation
35K70
Boundary estimate
35R03
Kolmogorov equation
Hypoelliptic
35K65
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Summary:We prove several new results concerning the boundary behavior of non-negative solutions to the equation Ku=0, whereK:=∑i=1m∂xixi+∑i=1mxi∂yi−∂t. Our results are established near the non-characteristic part of the boundary of certain local LipK-domains, where the latter is a class of local Lipschitz type domains adapted to the geometry of K. Generalizations to more general operators of Kolmogorov–Fokker–Planck type are also discussed. On démontre plusieurs nouveaux résultats sur le comportement au bord des solutions non négatives de l'équation Ku=0, oùK:=∑i=1m∂xixi+∑i=1mxi∂yi−∂t. Les résultats sont établis dans un voisinage de la partie non-caractéristique du bord de certains domaines locaux LipK, qui sont des domains localement lipschitziens adaptés à la géométrie de K. On discute aussi des généralisations à d'autres opérateurs plus généraux de type Kolmogorov–Fokker–Planck.
ISSN:0021-7824
1776-3371
DOI:10.1016/j.matpur.2016.02.007