This note concerns a nonlinear differential equation problem in which both the nonlinearity in the equation and its solution are determined by prescribed data. The question under consideration arises from a study of two-dimensional steady parallel-flows of a perfect fluid governed by Euler’s equations and a free-boundary condition, when the distribution of vorticity is arbitrary but prescribed.

We prove the existence of conformally parametrized minimizers for parametric two-dimensional variational problems subject to partially free boundary conditions. We establish regularity of class H loc ∩C1,α, 0 < α < 1, up to the free boundary under the assumption that there exists a perfect dominance function in the sense of C.B. Morrey. Mathematics Subject Classification (2000): 49J45, 49Q10, 4...

where f (p, 04-) is the Helmholz free energy density (HFED) in the limit ~, --~ 0; c~ = J" ~b(r)d~r; and fo(p) is the HFED for the case 'b = 0. It is shown rigorously that, for periodic boundary conditions, the conditional probability for a system in the grand canonical ensemble to violate the constraints at time t > 0, given that it satisfied them at time 0, is at most At, where 2~ is a quanti...

The propagation of torsional waves in a prestressed fiber-reinforced half-space under the effect of magnetic field and gravity has been discussed. The problem has been solved analytically using Whittaker function to obtain the exact solution frequency equations. Numerical results for stress, gravity and magnetic field are given and illustrated graphically. Comparisons are made with the results ...

Abstract. We study the diffusion limit of the Vlasov-Poisson-Fokker-Planck System. Here, we generalize the local in time results and the two dimensional results of Poupaud-Soler [F. Poupaud and J. Soler, Math. Models Methods Appl. Sci., 10(7), 1027-1045, 2000] and Goudon [T. Goudon, Math. Models Methods Appl. Sci., 15(5), 737-752, 2005] to the case of several space dimensions. Renormalization t...