Vega, Luis; Visciglia, Nicola On the local smoothing for a class of conformally invariant Schrödinger equations. (English) Zbl 1171.35117 Indiana Univ. Math. J. 56, No. 5, 2265-2304 (2007). The authors consider the Cauchy problems for certain linear and semilinear Schrödinger equations having the feature of being invariant under the conformal transformation. They prove a priori estimates from above and from below for solutions, which show a phenomenon of gain of \(\frac{1}{2}\) a derivative during the evolution. The techniques involved in the proves can be also used to obtain some new uniqueness results. Reviewer: Catalin Popa (Iaşi) Cited in 1 ReviewCited in 3 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 81U30 Dispersion theory, dispersion relations arising in quantum theory 35B45 A priori estimates in context of PDEs 35B65 Smoothness and regularity of solutions to PDEs Keywords:Schrödinger equation; conformal transformation; uniqueness of solutions PDFBibTeX XMLCite \textit{L. Vega} and \textit{N. Visciglia}, Indiana Univ. Math. J. 56, No. 5, 2265--2304 (2007; Zbl 1171.35117) Full Text: DOI arXiv