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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| Format: | Article |
| Language: | English |
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De Gruyter
2025-03-01
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| Series: | Advanced Nonlinear Studies |
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| 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. |
| format | Article |
| id | doaj-art-99d769ca38784e4093ec961e6b4cbb4b |
| institution | DOAJ |
| issn | 2169-0375 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT donghongjie globalschauderestimatesforkinetickolmogorovfokkerplanckequations AT yastrzhembskiytimur globalschauderestimatesforkinetickolmogorovfokkerplanckequations |