Partial Differential Equations

The research on partial differential equations can be divided into two subtopics: overdetermined problems and their numerical solution, and nonlinear potential theory.

Overdetermined problems occur both in pure and applied mathematics. The framework for analyzing such systems, the formal theory of partial differential equations, is based on considering a given equation as a submanifold in a suitable jet space. We have shown that the central concept of the theory, the involutive system, is also useful in the numerical solution of partial differential equations. This research is done in collaboration with Bijan Mohammadi (Université de Montpellier).

The algebraic tools which are also useful in the formal theory has also lead to the analysis of some constrained systems in multibody dynamics. Here the focus is on the analysis and characterization of possible singularities of the configuration space of the multibody system. This topic is studied in collaboration with Samuli Piipponen (University of Tampere) and Andreas Müller (Johannes Kepler Universität Linz).

The research on nonlinear potential theory concentrates on the regularity theory of solutions and supersolutions of nonlinear elliptic problems in metric spaces and in variable exponent spaces. In particular, the potential theoretic problems related to the fine topology are studied. The research related to the variable exponent is a part of the national research network Finnish variable exponent Sobolev spaces research group. The research on metric spaces is based on the co-operation with Anders and Jana Björn (Linköping University) and Tomasz Adamowicz (Institute of Mathematics, Polish Academy of Sciences).

RESEARCHERS OF PARTIAL DIFFERENTIAL EQUATIONS

Name: Position:
Gaëlle Brunet research assistant
Visa Latvala senior lecturer
Maryam Samavaki early stage researcher
Jukka Tuomela professor