Non Linear Singular Drifts and Fractional Operators: when Besov meets Morrey and Campanato

Diego Chamorro (1) , Stéphane Menozzi (2, 1)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
2 HSE - Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow]

Within the global setting of singular drifts in Morrey-Campanato spaces presented in [6], we study now the Hölder regularity properties of the solutions of a transport-diffusion equation with nonlinear singular drifts that satisfy a Besov stability property. We will see how this Besov information is relevant and how it allows to improve previous results. Moreover, in some particular cases we show that as the nonlinear drift becomes more regular, in the sense of Morrey-Campanato spaces, the additional Besov stability property will be less useful.

Keywords: Hölder regularity; Morrey-Campanato spaces; Besov spaces

Domains: Analysis of PDEs [math.AP]; Functional Analysis [math.FA]

Diego Chamorro, Stéphane Menozzi. Non Linear Singular Drifts and Fractional Operators: when Besov meets Morrey and Campanato. Potential Analysis, 2018, 49 (1), pp.1-35. ⟨hal-01383228v2⟩