My research interests include Partial Differential Equations, Calculus of Variations, Potential Theory and Harmonic Analysis.

In Partial Differential Equations and Potential Theory, I am working on the well-posedness of the Dirichlet problem for weighted elliptic quasi-linear equations specifically on unbounded domains, and its connection to boundary reguarity of infinity. This is joint work Ugur G. Abdulla.

In addition, I am analysing sharp and Diffuse interface models describing patterns on biological tissue in the framework of Γ--convergence in order to determine sub- and supercrititcal parameter regimes and macroscopic behaviour. This is joint work with Michael Bleher, Hans Knüpfer, Anna Marciniak-Czochra and Sebastian Nill.

Also, I am interested in generlisations of function spaces and commutator estimates on Riemannian geometry with techniques such as harmonic extensions and sharp estimates of square functions and maximal functions. This is joint work with Armin Schikorra.