We study the regularity properties of the second order linear degenerate parabolic operators. We prove that, if the operator Lsatisfies Hörmander’s hypoellipticity condition, and f is a Dini continuous function, then the second order derivatives of the solution u to the equation L u = f are Dini continuous functions as well. We also consider the case of Dini continuous coefficients of the secondo order derivatives. A key step in our proof is a Taylor formula for classical solutions to L u = f that we establish under minimal regularity assumptions on u.

Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients / Polidoro, Sergio; Rebucci, Annalaura; Stroffolini, Bianca. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 21:4(2022), pp. 1385-1416. [10.3934/cpaa.2022023]

Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients

Polidoro, Sergio
Membro del Collaboration Group
;
2022

Abstract

We study the regularity properties of the second order linear degenerate parabolic operators. We prove that, if the operator Lsatisfies Hörmander’s hypoellipticity condition, and f is a Dini continuous function, then the second order derivatives of the solution u to the equation L u = f are Dini continuous functions as well. We also consider the case of Dini continuous coefficients of the secondo order derivatives. A key step in our proof is a Taylor formula for classical solutions to L u = f that we establish under minimal regularity assumptions on u.
2022
18-gen-2022
21
4
1385
1416
Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients / Polidoro, Sergio; Rebucci, Annalaura; Stroffolini, Bianca. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 21:4(2022), pp. 1385-1416. [10.3934/cpaa.2022023]
Polidoro, Sergio; Rebucci, Annalaura; Stroffolini, Bianca
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1259217
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