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Browsing by Author "Naumann, Joachim"
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20051020BuchA Global LpGradient Estimate on Weak Solutions of Nonlinear Parabolic Systems under Mixed Boundary Conditions Naumann, Joachim; Wolff, MichaelIn 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 ...

20110811BuchA Meyers' type estimate for weak solutions to a generalized stationary NavierStokes system Druet, PierreÉtienne; Naumann, Joachim; Wolf, JörgIn 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 ...

20051021BuchInterior Integral Estimates on Weak Solutions of Nonlinear Parabolic Systems Naumann, Joachim; Wolff, MichaelThis 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 ...

20110811BuchMeasure and Integration on LipschitzManifolds 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 ...

20220701ZeitschriftenartikelOn the existence of global‐in‐time weak solutions and scaling laws for Kolmogorov's two‐equation model for turbulence Mielke, Alexander; Naumann, JoachimThis paper is concerned with Kolmogorov's twoequation model for turbulence in R 3 $\mathbb {R}^3$ involving the mean velocity u, the pressure p, an average frequency ω > 0 $\omega >0$ , and a mean turbulent kinetic energy ...

20020325BuchRemarks on the Prehistory of Sobolev Spaces Naumann, JoachimThe 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 ...

20051102BuchTransformation of Lebesgue Measure and Integral by Lipschitz Mappings Naumann, JoachimWe 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. ...