Professor of Mathematics at Aalto University School of Science. Address: Aalto University, School of Science and Technology, Department of Mathematics, P.O. Box 11100, FI-00076 Aalto, Finland. Tel: +358 50 430 5757. E-mail: juha.k.kinnunenaalto.fi.
The key area of research is mathematical analysis, or more precisely the theoretical aspects of non-linear partial differential equations. The main focus is on the 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 non-homogeneous media and the motions of multi-phased fluids in porous media. Methods from harmonic analysis are applied extensively and the research is also conducted in non-smooth contexts, ultimately in metric measure spaces.