Non linear singular drifts and fractional operators

Diego Chamorro () and Stéphane Menozzi ()
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Diego Chamorro: Université Paris-Saclay, Université d’Evry Val d’Essonne
Stéphane Menozzi: Université Paris-Saclay, Université d’Evry Val d’Essonne

Partial Differential Equations and Applications, 2024, vol. 5, issue 6, 1-39

Abstract: Abstract We consider parabolic PDEs associated with fractional type operators drifted by non-linear singular first order terms. When the drift enjoys some boundedness properties in appropriate Lebesgue and Besov spaces, we establish by exploiting a priori Besov-type estimates, the Hölder continuity of the solutions. In particular, we handle the almost critical case in whole generality.

Keywords: NonLinear PDE; Besov spaces; Hölder regularity; Hardy spaces; 35B65; 35K55 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42985-024-00302-1

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