%0 Journal Article %J Journal of Functional Analysis %D 2018 %T On fractional powers of singular perturbations of the Laplacian %A Vladimir Georgiev %A Alessandro Michelangeli %A Raffaele Scandone %K Point interactions %K Regular and singular component of a point-interaction operator %K Singular perturbations of the Laplacian %X

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.

%B Journal of Functional Analysis %V 275 %P 1551 - 1602 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123618301046 %R https://doi.org/10.1016/j.jfa.2018.03.007 %0 Journal Article %J Electron. J. Differential Equations (2004) 94 %D 2004 %T Solitary waves for Maxwell Schrodinger equations %A Giuseppe Maria Coclite %A Vladimir Georgiev %X 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. %B Electron. J. Differential Equations (2004) 94 %I SISSA Library %G en %U http://hdl.handle.net/1963/1582 %1 2536 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:52Z (GMT). No. of bitstreams: 1\\nmath.AP0303142.pdf: 326987 bytes, checksum: 37c172f10800ae7a41e5398f6a0a0a0e (MD5)\\n Previous issue date: 2002