KINETIC MAXIMAL Lp-REGULARITY FOR NONLOCAL KOLMOGOROV EQUATION AND APPLICATION Кинетическая максимальная Lp-регулярность для нелокального уравнения Колмогорова и ее применение
Trudy Instituta Matematiki i Mekhaniki UrO RAN, vol.31, no.1, pp.210-227, 2025 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 31 Issue: 1
- Publication Date: 2025
- Doi Number: 10.21538/0134-4889-2025-31-1-210-227
- Journal Name: Trudy Instituta Matematiki i Mekhaniki UrO RAN
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.210-227
- Keywords: anisotropic Sobolev spaces, dissipative operators, instantaneous smoothing, Kinetic maximal regularity, Kolmogorov equation, optimal Lp-estimates
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: No
Abstract
We study the linear and nonlinear variable coefficients Kolmogorov equations. The equations include the abstract operator A = A (x) in a Fourier type Banach space E and convolution terms. Here, the kinetic maximal Lp-regularity for the linear equatıon is derived in terms of E-valued Sobolev spaces. Moreover, we show that the solution u is also regular in time and space variables when u is assumed to have a certain amount of regularity in velocity. Finally, the kinetic maximal Lp-regularity for the linear equation can be used to obtain local existence and uniqueness of solutions to a quasilinear nonlocal Kolmogorov type kinetic equation.