Convex Hypersurfaces and $L^p$ Estimates for Schrödinger Equations

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70512This paper is concerned with Schrödinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the $L^p$-$L^q$ estimate of solution operator in free case. This estimate, combining with the results of fractionally integrated groups, allows us to further obtain the $L^p$ estimate of solutions for the initial data belonging to a dense subset of $L^p$ in the case of integrable potentials.18 pagesAnalysis of PDEsClassical Analysis and ODEs35J10; 42B10Convex Hypersurfaces and $L^p$ Estimates for Schrödinger Equationstext