Perturbed Sobolev spaces H^{s,p}_α admit an analogue description in terms of standard Sobolev spaces, extending Strichartz estimates and yielding local well-posedness for the singularly perturbed NLS in 2D and 3D.
Local well-pose dness and blow-up in the energy space for the 2d nls with point interaction
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Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the $L^p$ setting
Perturbed Sobolev spaces H^{s,p}_α admit an analogue description in terms of standard Sobolev spaces, extending Strichartz estimates and yielding local well-posedness for the singularly perturbed NLS in 2D and 3D.