Browsing by Author "Naumann, Joachim"

Now showing items 1-6 of 6

2005-10-20Buch

A Global Lp-Gradient Estimate on Weak Solutions of Nonlinear Parabolic Systems under Mixed Boundary Conditions

Naumann, Joachim; Wolff, Michael

In this paper, we prove the integrability of the spatial gradient Du to an exponent p>2 near the boundary, u being a weak solution of a nonlinear parabolic system under mixed boundary conditions. Our method of proof relies ...
2011-08-11Buch

A Meyers' type estimate for weak solutions to a generalized stationary Navier-Stokes system

Druet, Pierre-Étienne; Naumann, Joachim; Wolf, Jörg

In this paper, we prove a Meyers' type estimate for weak solutions to a Stokes system with bounded measurable coefficients in place of the usual constant viscosity. Besides the perturbation argument due to Meyers, we make ...
2005-10-21Buch

Interior Integral Estimates on Weak Solutions of Nonlinear Parabolic Systems

Naumann, Joachim; Wolff, Michael

This paper concerns various types of CACCIOPPOLI and POINCARÈ inequalities on weak solutions u of nonlinear parabolic systems. The main result of the paper is the local integrability of the spatial gradient Du to an exponent ...
2011-08-11Buch

Measure and Integration on Lipschitz-Manifolds

Naumann, Joachim; Simader, Christian G.

The first part of this paper is concerned with various definitions of a $k$-dimensional Lipschitz manifold ${\cal M}^k$ and a discussion of the equivalence of these definitions. The second part is then devoted to the ...
2002-03-25Buch

Remarks on the Prehistory of Sobolev Spaces

Naumann, Joachim

The paper gives a review on some works which led to the invention of the notion of "Sobolev space". Starting from works on the justification of the Dirichlet principle, we discuss a number of important contributions which ...
2005-11-02Buch

Transformation of Lebesgue Measure and Integral by Lipschitz Mappings

Naumann, Joachim

We first show that {\sc Lipschitz} mappings transform measurable sets into measurable sets. Then we prove the following theorem:\par {\it Let $E\subseteq \mathbb{R}^n$ be open, and let $\phi: E\to\mathbb{R}^n$ be continuous. ...