Heikki Johannes Jylhä
Ph.D. student @ Universitat Autònoma de Barcelona (UAB)
since 02/10/2016 for 1 year.
under the supervision of Prof. Albert Clop
Research
I finished my Masters degree in 2010 and my PhD degree in mathematics in 2014, both at the University of Jyväskylä. After that I participated in the program Optimal Transportation at the Hausdorff Research Institute for Mathematics in Bonn and worked as a Post Doc at the University of Jyväskylä. The main topic of my studies so far has been optimal transportation, in particular nonlinear L∞ optimal transport and limits of p-Laplace type equations and their connection to optimal transport. My current research focuses on the well-posedness of the Cauchy problem for linear transport and continuity equations with non-smooth vector fields, mostly in the case where the vector field has unbounded divergence. Of particular interest are vector fields with quasiconformal flows and the well-posedness in quasiconformally invariant spaces. Understanding these linear problems will give rise to methods which help deal with more complicated nonlinear equations, such as the Euler equation and the aggregation equation.
Complementary training activities:
- Language courses - A.A 2016-2017 Barcelona, Spain
Local training activities:
- Barcelona Analysis Conference 2016 - September 5-9, 2016 Barcelona, Spain
Network-wide training activities:
- Around Analysis, domains and mappings, conference on the occasion of the 75th birthday of Olli Martio - December 15-17, 2016 Jyväskylä, Finland
Talks and Poster Presentations:
- Talk: L∞ estimates in optimal transport at Barcelona Analysis Seminar - Frebrurary 8, 2016 Barcelona, Spain
- Talk: L∞ estimates in optimal transport at Follow-up Workshop to JTP 'Optimal Transportation' - August 29 to September 2,2016 Bonn, Germany
Secondment:
- TSS - January to October, 2017 Barcelona, Spain
Publications and Preprints
- H. Jylä, T. Rajala L∞ estimates in optimal mass transportation preprint
- A. Clop, H. Jylhä, J. Mateu, J. Orobitg Well-posedness for the continuity equation for vector fields with suitable modulus of continuity preprint
- H. Jylha Well-posedness for continuity equations for vector fields with Osgood modulus of continuity report
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