Qualitative properties of solutions for quasi-linear elliptic equations.
Cet article complète les résultats obtenus par J.-M. Bony et par l’auteur. On montre d’abord qu’on peut définir les fonctions harmoniques adjointes au faisceau donné, et qu’elles coïncident avec les solutions de l’équation adjointe. Puis, dans un ouvert assez régulier, la solution du problème de Dirichlet dans le cadre axiomatique est comparée à la solution au sens variationnel construite par M. Derridj.
We study the linearized water-wave problem in a bounded domain (e.g.a finite pond of water) of , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point of the water surface, where a submerged body touches the surface (see Fig. 1). The radiation...
We study the linearized water-wave problem in a bounded domain (e.g. a finite pond of water) of , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point of the water surface, where a submerged body touches the surface (see Fig. 1)....