I am presenting a survey of regularity results for both minima of variational integrals, and solutions to non-linear elliptic, and sometimes parabolic, systems of partial differential equations. I will try to take the reader to the Dark Side...
There is clear and incontrovertible evidence that the viscosity of many liquids depends on the pressure. While the density, as the pressure is increased by orders of magnitude, suffers small changes in its value, the viscosity changes dramatically. It can increase exponentially with pressure. In many fluids, there is also considerable evidence for the… (More)
We prove a maximum principle for linear second order elliptic systems in divergence form with discontinuous coefficients under a suitable condition on the dispersion of the eigenvalues of the coefficients matrix.
We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved. Résumé. Nous présentons une solution numérique deséquations d'Euler montrant la solution… (More)