Non Linear Singular Drifts and Fractional Operators: when Besov meets Morrey and Campanato
- 75 Downloads
Within the global setting of singular drifts in Morrey-Campanato spaces presented in Chamorro and Menozzi (Revista Matemática Iberoamericana 32(N∘4): 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.
KeywordsBesov spaces Morrey-Campanato spaces Hölder spaces
Mathematics Subject Classification (2010)Primary 35R09 35B65; Secondary 42B37
Unable to display preview. Download preview PDF.
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.
- 8.Coifmann, R., Weiss, G.: Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc., vol. 83 (1977)Google Scholar
- 11.Constantin, P., Wu, J.: Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations, Annales de l’Institut Henri Poincaré. Analyse non linéaire. N∘1 26, 159–180 (2009)Google Scholar
- 13.Delgadino, M.G., Smith, S.: Hölder estimates for fractional parabolic equations with critical divergence free drifts. arXiv:1609.02691v1 (2016)
- 15.Goldberg, D.: A local version of real Hardy spaces, Duke Mathematical Journal, Vol 46, N∘1 (1979)Google Scholar
- 16.Jacob, N.: Pseudo-Differential Operators and Markov Processes, Vol. I & II, Imperial College Press (2001)Google Scholar
- 22.Runst, T., Sickel, W.: Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations. De Gruyter series in nonlinear analysis and applications (1996)Google Scholar
- 24.Stein, E.M.: Harmonic Analysis. Princeton University Press (1993)Google Scholar
- 25.Torchinski, A.: Real-Variable methods in Harmonic Analysis. Dover (2004)Google Scholar