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math.AP2026
Point interactions and singular solutions to semilinear elliptic equations
Filippo Boni, Diego Noja, Raffaele Scandone
We investigate the connection between semilinear elliptic PDEs with isolated singularities and stationary nonlinear Schrödinger equations with point interactions. In dimensions $d…
math.AP2024
Energy cascade and Sobolev norms inflation for the quantum Euler equations on tori
Filippo Giuliani, Raffaele Scandone
In this paper we prove the existence of solutions to the quantum Euler equations on , , with almost constant mass density, displaying energy transfers t…