My research area is mathematical analysis, more precisely, theoretical aspects of nonlinear partial differential equations. The main focus is on regularity theory for a wide class of singular and degenerate elliptic and parabolic equations. These equations are connected to many different applications, such as diffusion in highly nonhomogeneous media and the motions of multiphased fluids in porous media. Methods from harmonic analysis are applied extensively and the research is also conducted in nonsmooth contexts, ultimately in metric measure spaces.

Bachelor, diploma and doctoral theses

I am glad to discuss possible topics for bachelor, diploma and doctoral theses. Please come and talk more with me, any time I am in my office M226.

Advanced courses in mathematical analysis

I offer courses as supported self study packages. Contents and material will be decided individually. For example, it may consist of lecture notes, books, research papers and regular appointments with the instructor. The grading is based on homework assignments, seminar presentations, home or oral exams. There are no particular prerequisites.

Topics include

Harmonic analysis (maximal functions, Muckenhoupt weights, Calderon-Zygmund theory, BMO) Modern real analysis Nonlinear partial differential equations (nonlinear parabolic equations, porous medium equation) Analysis on metric measure spaces (Sobolev spaces, minimizers and quasiminimizers for elliptic and parabolic variational problems, functions of bounded variation, minimal surfaces, variational problems with linear growth)

The Nonlinear PDE group website

The research group is based at Aalto University School of Science with close ties to several other Finnish and
foreign universities. In our research we rely heavily on group work and international collaboration.

Recent invited talks

Nonlinear Averaging and PDEs (Levico Terme 2019) - Partial Differential Equations in Analysis and Mathematical Physics (Cagliari 2019) - Beijing Normal University (2018) - Xi’an Jiaotong University (2018) - Research Term on Real Harmonic Analysis and its Applications to Partial Differential Equations and Geometric Measure Theory (ICMAT 2018) - New Developments in Nonlinear Partial Differential Equations (Bangalore 2017) - Equadiff 2017 (Bratislava) - Harnack’s Inequalities and Nonlinear Operators (Cortona 2017) - New Trends on Calculus of Variations and PDEs (Firenze-Montecatini 2017) - Around Analysis, Domains and Mappings (Jyväskylä 2016) - The Total Variation Flow and Related Nonlinear Evolution Problems (Salzburg 2016) - Workshop on Nonlinear PDEs (Sendai 2016) - Analysis and Geometry in Metric Spaces (ICMAT 2015) - Congreso de la RSME 2015 (Granada 2015) - Singular and Degenerate Evolution Problems (Cortona 2014) - Recent Advances in Nonlinear PDE and Calculus of Variations (Reading 2014)

Contact information

Aalto University, School of Science, Department of Mathematics and Systems Analysis
P.O. Box 11100, FI-00076 Aalto, Finland.
Phone :
+358 50 430 5757. Email:

Website at Aalto University:

Mathematics Genealogy Project and ResearchGate