# Juha Kinnunen

### Professor of Mathematics at Aalto University

## Research

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.

### J. Kinnunen, J. Lehrbäck and

A. Vähäkangas

A. Vähäkangas

**Maximal Function Methods for Sobolev Spaces**

### Mathematical Surveys and Monographs, 257. American Mathematical Society, 2021

## Recent invited talks

Nonlinear Analysis, Function Spaces and Applications (Prague 2022) - Advances in Evolution Equations and Applications (Pavia 2021) - Finnish Mathematical Days (Oulu 2020)- Swedish Summer PDEs (KTH 2019) - 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)

### Contact information

Aalto University, School of Science, Department of Mathematics

P.O. Box 11100, FI-00076 Aalto, Finland.

Phone : +358 50 430 5757. Email: juha.k.kinnunen@aalto.fi

Website at Aalto University: https://math.aalto.fi/en/people/juha.kinnunen