Publications
Sort:
Open Access Research Article Issue
On regularity and existence of weak solutions to nonlinear Kolmogorov-Fokker-Planck type equations with rough coefficients
Mathematics in Engineering 2023, 5(2): 1-37
Published: 15 April 2023
Abstract PDF (458.9 KB) Collect
Downloads:1

We consider nonlinear Kolmogorov-Fokker-Planck type equations of the form

(t+XY)u=X(A(Xu,X,Y,t)).

The function A=A(ξ,X,Y,t):Rm×Rm×Rm×RRm is assumed to be continuous with respect to ξ, and measurable with respect to X,Y and t. A=A(ξ,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 Hölder 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.

Total 1