Développement asymptotique de la densité d'états pour l'opérateur de Schrödinger aléatoire avec champ magnétique
We consider a function , , minimizing the integral , , where , or some more general functional with the same behaviour; we prove the existence of second weak derivatives and .
We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.
This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary. Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained. These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for homogeneous...