We consider degenerate Kolmogorov–Fokker–Planck operator such that the corresponding model operator having constant coefficients is hypoelliptic,translation invariant w.r.t.a Lie group operationi and 2-homogeneous w.r.t. a family of nonisotropic dilations. The coefficients are bounded and Dini continuous in space, and only bounded measurable in time. We prove that under some additional assumptions that the second derivatives of the solution are uniformly continuous in space and time.
KFP operators with coefficients measurable in time and Dini continuous in space / Biagi, S.; Bramanti, M.; Stroffolini, B.. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 24:2(2024), pp. 1-52. [10.1007/s00028-024-00964-9]
KFP operators with coefficients measurable in time and Dini continuous in space
Stroffolini B.
2024
Abstract
We consider degenerate Kolmogorov–Fokker–Planck operator such that the corresponding model operator having constant coefficients is hypoelliptic,translation invariant w.r.t.a Lie group operationi and 2-homogeneous w.r.t. a family of nonisotropic dilations. The coefficients are bounded and Dini continuous in space, and only bounded measurable in time. We prove that under some additional assumptions that the second derivatives of the solution are uniformly continuous in space and time.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.