Remarks on the Navier-Stokes equations
Travelling fronts in cylinders
Further qualitative properties for elliptic equations in unbounded domains
A geometric problem and the Hopf Lemma. I
A classical result of A. D. Alexandrov states that a connected compact smooth -dimensional manifold without boundary, embedded in , and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of in a hyperplane in case satisfies: for any two points , on , with , the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional condition for . Some variations...
The Dirichlet problem for the degenerate Monge-Ampère equation.
Let Ω be a bounded convex domain in Rn with smooth, strictly convex boundary ∂Ω, i.e. the principal curvatures of ∂Ω are all positive. We study the problem of finding a convex function u in Ω such that: det (uij) = 0 in Ω u = φ given on ∂Ω.
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