Michael Bildhauer

Partial regularity for a class of anisotropic variational integrals with convex hull property

We consider integrands f:\mathbb{R}^{nN}\rightarrow\mathbb{R} which are of lower (upper) growth rate s\geq2(q>s) and which satisfy an additional structural condition implying the convex hull property, i.e. if the boundary data of a minimizer u:\Omega\rightarrow\mathbb{R}^{N} of the energy \int_{\Omega}f(\nabla u)dx respect a closed convex set K\subset\mathbb{R}^{N}, then so does u on the whole domain. We show partial C^{1,\alpha}-regularity of bounded local minimizers if q<min\{s+\frac{2}{3},s\frac{n}{n-2}\} and discuss cases in which the latter condition on the exponents can be improved. Moreover, we give examples of integrands which fit into our category and to which the results of Acerbi and Fusco [AF2] do not apply, in particular, we give some extensions to the subquadratic case.

Variants of the Stokes Problem: the Case of Anisotropic Potentials

AbstractWe investigate the smoothness properties of local solutions of the nonlinear Stokes problem

A regularity theory for scalar local minimizers of splitting-type variational integrals

\begin{eqnarray*}-\diverg \{T(\eps(v))\} + \nabla \pi &=& g \msp \mbox{on

Elliptic Variational Problems with Nonstandard Growth

\Omega

Two dimensional variational problems with linear growth

,}\\\diverg v&\equiv & 0 \msp \mbox{on

On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids

\Omega

Relaxation of convex variational problems with linear growth defined on classes of vector-valued functions

,}\end{eqnarray*}

DUALITY BASED A POSTERIORI ERROR ESTIMATES FOR HIGHER ORDER VARIATIONAL INEQUALITIES WITH POWER GROWTH FUNCTIONALS

where v: Ω → ℝn is the velocity field,

Twodimensional anisotropic variational problems

\pi

Higher order variational problems on two-dimensional domains

: Ω → ℝ