Carsten Ebmeyer

Optimal Convergence for the Implicit Space-Time Discretization of Parabolic Systems with

Parabolic systems with

p

p

-Structure

-structure are considered on convex polyhedral domains under Dirichlet boundary conditions. A fully discrete scheme is studied using

Global Regularity in Fractional Order Sobolev Spaces for the p-Laplace Equation on Polyhedral Domains

C^0

Quasi-Norm interpolation error estimates for the piecewise linear finite element approximation of p -Laplacian problems

-piecewise linear finite elements in space and the backward Euler difference scheme in time. A priori error estimates in quasi norms are proved, and optimal convergence rates are obtained.

Mixed Boundary Value Problems for Nonlinear Elliptic Systems withp-Structure in Polyhedral Domains

The p-Laplace equation is considered for p > 2 on a n-dimensional convex polyhedral domain under a Dirichlet boundary value condition. Global regularity of weak solutions in weighted Sobolev spaces and in fractional order Nikolskij and Sobolev spaces are proven

Regularity in Sobolev spaces for doubly nonlinear parabolic equations

Summary.In this work, new interpolation error estimates have been derived for some well-known interpolators in the quasi-norms. The estimates are found to be essential to obtain the optimal a priori error bounds under the weakened regularity conditions for the piecewise linear finite element approximation of a class of degenerate equations. In particular, by using these estimates, we can close the existing gap between the regularity required for deriving the optimal error bounds and the regularity achievable for the smooth data for the 2-d and 3-dp-Laplacian.

Finite Element Approximation of the Fast Diffusion and the Porous Medium Equations

The nonlinear elliptic system is investigated on a non-smooth domain. Mixed boundary value conditions are given. The left-hand side of the system has p-structure (e.g., it is the p-Laplacian and 1 < p < ∞). Global regularity results of u and |∇u|p/2 in fractional order Sobolev spaces are proven.

The smoothing property for a class of doubly nonlinear parabolic equations

Abstract The doubly nonlinear parabolic equation u t = div [| ∇ (|u| m−1 u)| p−2 ∇ (|u| m−1 u)] (m>1,m(p−1)>1) is considered in several dimensions and regularity results in fractional order Sobolev spaces are obtained. The main tools in the proof are a difference quotient technique and the imbedding theorem of Nikolskii spaces into Sobolev spaces.

Global Regularity in Sobolev Spaces for Elliptic Problems with p-structure on Bounded Domains

1The fast diffusion equation