Une formule de Landau-Zener pour un croisement générique de codimension 2
The aim of this work is to give a Gårding inequality for pseudodifferential operators acting on functions in supported in a closed regular region . A natural idea is to suppose that the symbol is non-negative in . Assuming this, we show that this result is true for pseudo-differential operators of order one, when is the half-space, and under a supplementary weak hypothesis of degeneracy of the symbol on the boundary.
The aim of the paper is to give a method to solve boundary value problems associated to the Helmholtz equation and to the operator of elasticity. We transform these problems in problems on the boundary Gamma of an open set of R3. After introducing a symplectic form on H1,2(G) x H-1,2(G) we obtain the adjoint of the boundary operator employed. Then the boundary problem has a solution if and only if the boundary conditions are orthogonal, for this bilinear form, to the elements of the kernel, in a...
In this paper, we consider second order neutrons diffusion problem with coefficients in L∞(Ω). Nodal method of the lowest order is applied to approximate the problem's solution. The approximation uses special basis functions [1] in which the coefficients appear. The rate of convergence obtained is O(h2) in L2(Ω), with a free rectangular triangulation.