Agirre, Mikel; Vega, Luis Some lower bounds for solutions of Schrödinger evolutions. (English) Zbl 1419.35170 SIAM J. Math. Anal. 51, No. 4, 3324-3336 (2019). Summary: We present some lower bounds for regular solutions of Schrödinger equations with bounded and time dependent complex potentials. Assuming that the solution has some positive mass at time zero within a ball of certain radius, we prove that this mass can be observed if one looks at the solution and its gradient in space-time regions outside of that ball. Cited in 4 Documents MSC: 35Q41 Time-dependent Schrödinger equations and Dirac equations 39A12 Discrete version of topics in analysis Keywords:Schrödinger; PDE; uniqueness PDFBibTeX XMLCite \textit{M. Agirre} and \textit{L. Vega}, SIAM J. Math. Anal. 51, No. 4, 3324--3336 (2019; Zbl 1419.35170) Full Text: DOI arXiv References: [1] N. Anantharaman and F. Macià, Semiclassical measures for the Schrödinger equation on the torus, J. Eur. Math. Soc. (JEMS), 16 (2014), pp. 1253-1288. · Zbl 1298.42028 [2] J. Bourgain, N. Burq, and M. Zworski, Control for Schrödinger operators on 2-tori: Rough potentials, J. Eur. Math. Soc. (JEMS), 15 (2013), pp. 1597-1628. · Zbl 1279.35016 [3] N. Burq and M. Zworski, Control for Schrödinger operators on tori, Math. Res. Lett., 19 (2012), pp. 309-324. · Zbl 1281.35011 [4] L. Escauriaza, C.E. Kenig, and G. Ponce, Hardy’s uncertainty principle, convexity and Schrödinger evolutions, J. Eur. Math. Soc. (JEMS), 10 (2008), pp. 883-907. · Zbl 1158.35018 [5] L. Escauriaza, C.E. Kenig, G. Ponce, and L. Vega, On uniqueness properties of solutions of Schrödinger equations, Comm. Partial Differential Equations, 31 (2006), pp. 1811-1823. · Zbl 1124.35068 [6] L. Escauriaza, C.E. Kenig, G. Ponce, and L. Vega, Uniqueness properties of solutions to Schrödinger equations, Bull. Amer. Math. Soc. (N.S.), 49 (2012), pp. 415-442. · Zbl 1268.35112 [7] C.E. Kenig, G. Ponce, and L. Vega, A theorem of Paley-Wiener type for Schrödinger evolutions, Ann. Sci. Éc. Norm. Super. (4), 47 (2014), pp. 539-557. · Zbl 1308.35274 [8] F. Nazarov, Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type, St. Petersburg Math. J., 5 (1994), pp. 663-717. · Zbl 0822.42001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.