Joachim Naumann

Interior Integral Estimates on Weak Solutions of Nonlinear Parabolic Systems

This paper concerns various types of CACCIOPPOLI and POINCAR E 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 p

A uniqueness theorem for weak solutions of the stationary semiconductor equations

In this paper we prove a uniqueness theorem for weak solutions of a mixed boundary-value problem for the stationary semiconductor equations (van Roosbroecks system) under the assumption that the deviation of the carrier potentials from an equilibrium solution is sufficiently small.

Interior integral estimates on weak solutions of certain degenerate elliptic systems

SummaryWe prove the existence of second order derivatives of any weak solution of the system

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

\frac{\partial }{{\partial x_\alpha }}A_i^\alpha (\nabla u) = 0(i = 1,...,N)

Existence of Weak Solutions of an Unsteady Thermistor System with p -Laplacian Type Equation

under very mild conditions on the functions Aiα. These conditions include the special case: Aiα(ξ)=0 if ξ=0, Aiα(ξ)=|ξ|p−2ξiα if ξ≠0 (ξ∈ℝnN;α=1,...,n,i=1,...,N;1<p<2). Under a stronger condition on Aiα we establish an appropriate Caccioppoli inequality which enables us to prove the integrability of (1+|∇u|2)(p−1)/4 ∇2u to a certain power t > 2.

On Weak Solutions to the Non-stationary van Roosbroeck's System with Discontinuous Permittivities

SuntoNel presente lavoro si considera il sistema del moto stazionario di un fluido incompressibile

On the existence of weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids

\begin{gathered} - \frac{\partial }{{\partial x_j }}S_{ij} (D(u)) + \frac{{\partial p}}{{\partial x_i }} = f_i (i = 1,2,3), \hfill \\ div u = 0 \hfill \\ \end{gathered}