Nonlinear PDE research group

In our research we consider a large and important class of singular and degenerate non-linear partial differential equations (PDEs) ranging from flows by mean curvature to the infinity Laplacian. Such PDEs have a common structure, yet they are connected to many different applications like the diffusion in highly non-homogeneous and anisotropic media, the motion of multi-phase fluids and flow through a porous media. The velocity gradient of these fluids depends in non-linear way on the stress tensor as occurs, for instance, in glaceology, rheology, mean curvature flow and non-linear elasticity. Other applications include behavior of composite materials, image processing, stochastic game theory, and pricing the assets in financial markets. We focus on four themes

• Parabolic PDEs
• PDEs with non-standard growth
• PDEs in limiting cases and
• PDEs on metric measure spaces

The project receives long term funding from

• The Academy of Finland (2007-2010, 2010-2014)
• The Emil Aaltonen Foundation (2007-2009)

Shorter-term funding has been provided on several occasions by

• The Academy of Finland
• The Finnish Academy of Science and Letters, Vilho, Yrjö and Kalle Väisälä Foundation
• The Finnish Society of Sciences and Letters, Magnus Ehrnrooth Foundation
• Finnish National Graduate School in Mathematical Analysis and Its Applications