Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations

We present global Schauder type estimates in all variables and unique solvability results in kinetic Hölder spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equations. The leading coefficients are Hölder continuous in the x, v variables and are merely measurable in the temporal variable. Our proof...

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Main Authors: Dong Hongjie, Yastrzhembskiy Timur
Format: Article
Language:English
Published: De Gruyter 2025-03-01
Series:Advanced Nonlinear Studies
Subjects:
Online Access:https://doi.org/10.1515/ans-2023-0167
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author Dong Hongjie
Yastrzhembskiy Timur
author_facet Dong Hongjie
Yastrzhembskiy Timur
author_sort Dong Hongjie
collection DOAJ
description We present global Schauder type estimates in all variables and unique solvability results in kinetic Hölder spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equations. The leading coefficients are Hölder continuous in the x, v variables and are merely measurable in the temporal variable. Our proof is inspired by Campanato’s approach to Schauder estimates and does not rely on the estimates of the fundamental solution of the KFP operator.
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publishDate 2025-03-01
publisher De Gruyter
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series Advanced Nonlinear Studies
spelling doaj-art-99d769ca38784e4093ec961e6b4cbb4b2025-08-20T03:12:34ZengDe GruyterAdvanced Nonlinear Studies2169-03752025-03-0125242245510.1515/ans-2023-0167Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equationsDong Hongjie0Yastrzhembskiy Timur1Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI02912, USAUniversity of Wisconsin-Madison, Madison, WI53706, USAWe present global Schauder type estimates in all variables and unique solvability results in kinetic Hölder spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equations. The leading coefficients are Hölder continuous in the x, v variables and are merely measurable in the temporal variable. Our proof is inspired by Campanato’s approach to Schauder estimates and does not rely on the estimates of the fundamental solution of the KFP operator.https://doi.org/10.1515/ans-2023-0167kinetic kolmogorov-fokker-planck equationsschauder estimatescampanato’s methodtime irregular coefficients35k7035h1035b4535k1535r05
spellingShingle Dong Hongjie
Yastrzhembskiy Timur
Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations
Advanced Nonlinear Studies
kinetic kolmogorov-fokker-planck equations
schauder estimates
campanato’s method
time irregular coefficients
35k70
35h10
35b45
35k15
35r05
title Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations
title_full Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations
title_fullStr Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations
title_full_unstemmed Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations
title_short Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations
title_sort global schauder estimates for kinetic kolmogorov fokker planck equations
topic kinetic kolmogorov-fokker-planck equations
schauder estimates
campanato’s method
time irregular coefficients
35k70
35h10
35b45
35k15
35r05
url https://doi.org/10.1515/ans-2023-0167
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