Daniel Lengeler

The Stokes and Poisson problem in variable exponent spaces

We study the Stokes and Poisson problem in the context of variable exponent spaces. We prove existence of strong and weak solutions for bounded domains with a C 1,1 boundary with inhomogeneous boundary values. The result is based on generalizations of the classical theories of Calderón–Zygmund and Agmon–Douglis–Nirenberg to variable exponent spaces.

Partial Regularity for Minimizers of Quasi-convex Functionals with General Growth

We prove a partial regularity result for local minimizers of quasiconvex variational integrals with general growth. The main tool is an improved A-harmonic approximation, which should be interesting also for classical growth.The convex hull property is the natural generalization of maximum principles from scalar to vector valued functions. Maximum principles for finite element approximations are often crucial for the preservation of qualitative properties of the respective physical model. In this work we develop a convex hull property for

Functional setting for unsteady problems in moving domains and applications

\mathbb{P }_1

Global weak solutions for an incompressible Newtonian fluid interacting with a linearly elastic Koiter shell

conforming finite elements on simplicial non-obtuse meshes. The proof does not resort to linear structures of partial differential equations but directly addresses properties of the minimiser of a convex energy functional. Therefore, the result holds for very general nonlinear partial differential equations including e.g. the

Global weak solutions for an incompressible, generalized Newtonian fluid interacting with a linearly elastic Koiter shell

p

Asymptotic stability of local Helfrich minimizers

-Laplacian and the mean curvature problem. In the case of scalar equations the introduce techniques can be used to prove standard discrete maximum principles for nonlinear problems. We conclude by proving a strong discrete convex hull property on strictly acute triangulations.