naa a22 4500 510760694 CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s13163-012-0100-4 doi (NATIONALLICENCE)springer-10.1007/s13163-012-0100-4 Puel Jean-Pierre Ikerbasque & Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500, 48160, Derio, Basque Country, Spain aut A regularity property for Schrödinger equations on bounded domains [Elektronische Daten] [Jean-Pierre Puel] We give a regularity result for the free Schrödinger equations set in a bounded domain of ℝ N which extends the 1-dimensional result proved in Beauchard and Laurent (J. Math. Pures Appl. 94(5):520-554, 2010) with different arguments. We also give other equivalent results, for example, for the free Schrödinger equation, if the initial value is in $H^{1}_{0}(\varOmega)$ and the right hand side f can be decomposed in f=g+h where $g\in L^{1}(0,T;H^{1}_{0}(\varOmega))$ and h∈L 2(0,T;L 2(Ω)), Δh=0 and h /Γ ∈L 2(0,T;L 2(Γ)), then the solution is in $C([0,T];H^{1}_{0}(\varOmega))$ . This obviously contains the case f∈L 2(0,T;H 1(Ω)). This result is essential for controllability purposes in the 1-dimensional case as shown in Beauchard and Laurent (J. Math. Pures Appl. 94(5):520-554, 2010) and might be interesting for the N-dimensional case where the controllability problem is open. Revista Matemática Complutense, 2012 Schrödinger equations nationallicence Regularity nationallicence Multiplier method nationallicence Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 183-192 1139-1138 26:1<183 2013 26 13163 https://doi.org/10.1007/s13163-012-0100-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-012-0100-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Puel Jean-Pierre Ikerbasque & Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500, 48160, Derio, Basque Country, Spain aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 183-192 1139-1138 26:1<183 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer