There are three kinds of food. One is the food that your mother makes for you. One is the kind
of food that you eat in restaurants. One is the kind of food that you eat in dreams.
— Kelly Link: The Girl Detective
InterestsI am an expert on partial differential equations and the calculus of variations.
I am interested in using the optimal control theory, dynamical optimisation methods and other mathematical tools in environmental and resource economics.
I teach mathematics for economists.
Papers & Preprints
7. Improved Hölder regularity for strongly elliptic PDEs (with Kari Astala, Albert Clop, Daniel Faraco and Aleksis Koski), Journal de Mathématiques Pures et Appliquées (2020) 140: 230–258, doi:10.1016/j.matpur.2020.06.005, preprint in arXiv:1906.10906
6. The Radó-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces (with Tomasz Adamowicz and Aleksis Koski), Revista Matemática Iberoamericana, (2020) 36 (6): 1779–1834, doi:10.4171/rmi/1183, postprint in JYX, preprint in arXiv:1806.03020
5. Nonlinear Beltrami operators, Schauder estimates and bounds for the Jacobian (with Kari Astala, Albert Clop, Daniel Faraco and Aleksis Koski), Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire (2017) 34 (6): 1543–1559, doi:10.1016/j.anihpc.2016.10.008, preprint in arXiv:1511.08370
4. Manifolds of quasiconformal mappings and the nonlinear Beltrami equation (with Kari Astala, Albert Clop and Daniel Faraco), Journal d'Analyse Mathematique (2019) 139 (1): 207–238, doi:10.1007/s11854-019-0059-x, postprint in JYX, preprint in arXiv:1412.4046
3. Uniqueness of Normalized Homeomorphic Solutions to Nonlinear Beltrami Equations (with Kari Astala, Albert Clop, Daniel Faraco and László Székelyhidi Jr.), International Mathematics Research Notices IMRN (2012) 2012 (18): 4101–4119, doi:10.1093/imrn/rnr178, preprint in arXiv:1012.2827
2. On reduced Beltrami equations and linear families of quasiregular mappings, Journal für die reine und angewandte Mathematik (Crelles Journal) (2013) 682: 49–64, doi:10.1515/crelle-2012-0041, preprint in arXiv:1009.2614
1. Homeomorphic solutions to reduced Beltrami equations (with Kari Astala), Annales Academiæ Scientiarum Fennicæ Mathematica (2009) 34: 607–613, preprint in
arXiv:0812.2322
DissertationOn Linear and Nonlinear Beltrami Systems, Ph.D. dissertation, University of Helsinki, collecting papers 1.–3. [handout slides of Lectio praecursoria]
