Abstract: 
I will discuss the well posedness of the nonlinear Schrodinger equation with power-type nonlinearity and in the presence of a delta interaction, both in dimension two and three. This is a model of evolution for some singular solutions that are well known in the analysis of semilinear elliptic equations. I will consider local existence, uniqueness and continuous dependence from the initial data of strong (operator domain) solutions of the associated Cauchy problem. In dimension two well posedness holds for any power nonlinearity and global existence is proved for powers below the cubic. In dimension three local and global well posedness are restricted to low powers. 
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The talk is based on a joint work with Domenico Finco and Diego Noja.