We sketch a proof of the fact that the Gromov boundary of a hyperbolic group does not have a global cut point if it is connected. This implies, by a theorem of Bestvina and Mess, that the boundary is locally connected if it is connected. The object of this note is to sketch a proof of the following theorem: Theorem 1. If ? is a one ended hyperbolic group, then the Gromov boundary @? of ? does n...

We study the questions of existence and uniqueness of non-negative solutions to the Cauchy problem    ρ(x) ∂tu = ∆um in Q := Rn × R+ u(x, 0) = u0 in dimensions n ≥ 3. We deal with a class of solutions having finite energy

where u and 4~ denote scalar functions on R 2, and g is a scalar function on R. We shall assume g and ff continuous, and we shall determine sufficient conditions in the form of inequalities to guarantee that problem (1) has continuous solutions. Thus, the solutions which we consider will be weak solutions in the sense of distributions. In terms of functional analysis and the alternative approac...

The Cauchy problem for the Korteweg-deVdes equation is considered with initial profile integrable against (1 + Ix[) dx on R and against (1 + ]x]) dx on R+. Classical solutions are constructed for N => 11/4. Under mild additional hypotheses the solution evolves in L2().

We derive the equation for the vorticity of the incompressible Oseen problem in a half plane with homogeneous (no slip) boundary conditions. The resulting equation is a scalar Oseen equation with certain Dirichlet boundary conditions which are determined by the incompressibility condition and the boundary conditions of the original problem. We prove existence and uniqueness of solutions for thi...