Renijin Jiang
Post Doc @ Universitat Autònoma de Barcelona (UAB)
since 11/14/2014 for 1 year.
under the supervision of Prof. Albert Clop
Research
The studies are about: 1) the well-posednes/ill-posedness of the transport equations, and flows for the non-smooth vector fields with borderline integral divergence, 2) quasiconformal flows and the well-posedness of the transport equation in quasi-conformally invariant spaces, 3) applications of the transport equation to Euler type fluid equations.
Local training activities:
- periodic Seminar of Analysis in Barcelona - A.A 2014/15 Barcelona, Spain
- Reading course: Elliptic Partial Differential Equations, - A.A 2014/15 Barcelona, Spain
Talks and Poster Presentations:
- Heat Kernels and Harmonic Functions on Metric Measure Spaces at Conference on Analysis and Geometry - August 4-9, 2015 Hefei, Anhui, China
- On the equivalence of quantitative regularity of harmonic functions and heat kernels and its applications at periodic Jyväskylä Analysis Seminar - A.A 2015/16 Jyväskylä, Finland
Network-wide training activities:
- Workshop on Analysis and Geometry in metric spaces - June 1-5, 2015 Madrid, Spain
- Geometric mesaure theory, optimal mass transportation and PDEs - June 15-19, 2015 Sant Feliu de Guíxols, Spain
Publications and Preprints
- Y. Liang, D. Yang, R.Jiang Weak Musielak–Orlicz Hardy spaces and applications on Mathematische Nachrichten Vol 289, issue 5-6 Wiley-VCH Verlag 2015 pp. 634-677
- A. Clop, R. Jiang, J. Mateu, J. Orobitg, Linear transport equations for vector fields with subexponentially integrable divergence on Calculus of Variations and Partial Differential Equations Vol 55, issue 1 Springer New York 2016 pp. 21-55 open access version
- A. Clop, R. Jiang, J. Mateu, J. Orobitg Flows for non-smooth vector fields with subexponentially integrable divergence on Journal of Differential Equations Vol 261, issue 2 /*Elsevier */ 2016 pp. 1237-1263 open access version
- R. Jiang, H. C. Zhangg Hamilton’s gradient estimates and a monotonicity formula for heat flows on metric measure spaces on Nonlinear Analysis, Theory, Methods and Applications Vol 131 /*Elsevier */ 2016 pp. 32-47 open access version
- A. Clop, R. Jiang, J. Mateu, J. Orobitg A Note on Transport Equation in Quasiconformally Invariant Spaces preprint
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