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Potential Analysis

, Volume 49, Issue 1, pp 1–35 | Cite as

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

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Abstract

Within the global setting of singular drifts in Morrey-Campanato spaces presented in Chamorro and Menozzi (Revista Matemática Iberoamericana 32(N4): 1445–1499 2016), 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

Besov spaces Morrey-Campanato spaces Hölder spaces 

Mathematics Subject Classification (2010)

Primary 35R09 35B65; Secondary 42B37 

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Notes

Acknowledgments

We kindly acknowledge the two anonymous referees for their careful reading and comments which helped improving the manuscript.

For the second author, the article was prepared within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Modélisation d’Evry, CNRS UMR 8071Université d’Evry Val d’EssonneEvryFrance
  2. 2.Laboratory of Stochastic Analysis, HSEMoscowRussia

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