Boletim Da Sociedade Brasileira De Matematica 

About: Boletim Da Sociedade Brasileira De Matematica is an academic journal. The journal publishes majorly in the area(s): Scalar curvature & Curvature. Over the lifetime, 431 publications have been published receiving 8196 citations.

On the method of moving planes and the sliding method

Abstract: The method of moving planes and the sliding method are used in proving mono- tonicity or symmetry in, say, the zl direction "for solutions of nonlinear elliptic equations F(x, u, Du, D~u) = 0 in a bounded domain (2 in R n which is convex in the Zl direction. Here we present a much simplified approach to these methods; at the same time it yields improved results. For example, for the Dirichlet problem, no regularity of the boundary is assumed. The new approach relies on improved forms of the Maximum Principle in "narrow domains". Several results are also presented in cylindrical domains -- under more general boundary conditions.

Lagrangian flows: The dynamics of globally minimizing orbits

Abstract: The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications. We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma].

Strong solutions of the Navier-Stokes equation in Morrey spaces

Abstract: It is shown that the nonstationary Navier-Stokes equation (NS) in ℝ+×ℝ m is well posed in certain Morrey spacesM p,λ (ℝ+×ℝ m ) (see the text for the definition: in particularM p,0=L p ifp>1 andM 1,0 is the space of finite measures), in the following sense. Given a vectora∈M p,m-p with diva=0 and with certain supplementary conditions, there is a unique local (in time) solution (velocity field)u(t, ·)∈M p, m-p, which is smooth fort>0 and takes the initial valuea at least in a weak sense.u is a global solution ifa is sufficiently small. Of particular interest is the spaceM 1,m−1, which admits certain measures; thusa may be a surface measure on a smooth (m−1)- dimensional surface in ℝ+×ℝ m . The regularity of solutions and the decay of global solutions are also considered. The associated vorticity equation (for the vorticity ζ=∂∧u) can similarly be solved in (tensor-valued)M 1,m−2, which is also a space of measures of another kind.