We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

VL - 275 UR - http://www.sciencedirect.com/science/article/pii/S0022123618301046 ER - TY - JOUR T1 - Solitary waves for Maxwell Schrodinger equations JF - Electron. J. Differential Equations (2004) 94 Y1 - 2004 A1 - Giuseppe Maria Coclite A1 - Vladimir Georgiev AB - In this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated. PB - SISSA Library UR - http://hdl.handle.net/1963/1582 U1 - 2536 U2 - Mathematics U3 - Functional Analysis and Applications ER -