Pointwise estimates for degenerate Kolmogorov equations with \(L^p\)-source term. (English) Zbl 1487.35134
Main goal of the authors is the study pointwise regularity of solutions to a problem related to a degenerate second-order partial differential equation involving a Kolmogorov-type operator \(L\).
This study could be considered as a generalization of previous ones, where this kind of results are obtained for elliptic and parabolic equations.
The main difficulty with respect to the previous literature lies in the fact that the regularity properties of the Kolmogorov equations on \(\mathbb{R}^{N +1}\) depend strongly on the geometric Lie group structure. Specifically this reflects on the family of dilations which are considered.
This study could be considered as a generalization of previous ones, where this kind of results are obtained for elliptic and parabolic equations.
The main difficulty with respect to the previous literature lies in the fact that the regularity properties of the Kolmogorov equations on \(\mathbb{R}^{N +1}\) depend strongly on the geometric Lie group structure. Specifically this reflects on the family of dilations which are considered.
Reviewer: Maria Alessandra Ragusa (Catania)
MSC:
| 35B45 | A priori estimates in context of PDEs |
| 35B44 | Blow-up in context of PDEs |
| 35K70 | Ultraparabolic equations, pseudoparabolic equations, etc. |
| 35K65 | Degenerate parabolic equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Keywords:
degenerate Kolmogorov equation; Dini regularity; pointwise regularity; BMO pointwise estimate; VMO pointwise estimateReferences:
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