On regularity and existence of weak solutions to nonlinear Kolmogorov-Fokker-Planck type equations with rough coefficients

被引:0
|
作者
Garain, Prashanta [1 ]
Nystrom, Kaj [1 ]
机构
[1] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden
来源
MATHEMATICS IN ENGINEERING | 2023年 / 5卷 / 02期
关键词
Kolmogorov equation; parabolic; ultraparabolic; hypoelliptic; nonlinear Kolmogorov-Fokker-Planck equations; existence; uniqueness; regularity; C-ALPHA REGULARITY; ULTRAPARABOLIC EQUATIONS; H-THEOREM; BOLTZMANN; OPERATORS;
D O I
10.3934/mine.2023043
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider nonlinear Kolmogorov-Fokker-Planck type equations of the form (partial derivative(t) + X . del(Y))(u) = del(X) . (A(del(X)u, X, Y, t)). The function A = A(xi, X, Y, t) : R-m x R-m x R-m x R -> R-m is assumed to be continuous with respect to xi, and measurable with respect to X, Y and t. A = A(xi, X, Y, t) is allowed to be nonlinear but with linear growth. We establish higher integrability and local boundedness of weak sub-solutions, weak Harnack and Harnack inequalities, and Holder continuity with quantitative estimates. In addition we establish existence and uniqueness of weak solutions to a Dirichlet problem in certain bounded X, Y and t dependent domains.
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页码:1 / 37
页数:37
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