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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)
The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral… (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.
After exposure for several days of intensively growing algal cultures to a radium concentration of 10(-6) g.1(-1) the physiological and genetic responses of Chlorella kessleri and Scenedesmus obliquus cells could be clearly demonstrated. Of physiological characteristics, we recorded the frequency of cells with a reduced number of autospores, the length of… (More)
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)