A New Carleman Inequality for a Linear Schrödinger Equation on Some Unbounded Domains

TORRES, PABLO; CONSTANZA SÁNCHEZ FERNÁNDEZ DE LA VEGA; DE TERESA, LUZ

APPLIED MATHEMATICS AND OPTIMIZATION

SPRINGER

Lugar: Berlin; Año: 2022 vol. 87

0095-4616

This article presents a new Carleman inequality for a linear Schrödinger equation which is suitable for both bounded and unbounded domains. We characterize the conditions on the auxiliary function necessary to obtain the global inequality. The novelty of this result is the construction of the auxiliary function on some unbounded domains and for a corresponding valid control region 𝜔. As a consequence, we prove some results on the controllability of a linear Schrödinger equation on unbounded domains.