Uniqueness Properties of Solutions to Schr\"odinger Equations
Luis Escauriaza, Carlos E. Kenig, Gustavo Ponce, Luis Vega
TL;DR
This paper reviews recent results on the unique continuation properties of solutions to Schrödinger equations, including both linear and semi-linear cases with time-dependent potentials.
Contribution
It provides a comprehensive review of new findings related to the uniqueness and continuation properties of Schrödinger equation solutions.
Findings
Established new unique continuation results for linear Schrödinger equations with time-dependent potentials.
Extended unique continuation properties to semi-linear Schrödinger equations.
Reviewed recent advances in the mathematical understanding of Schrödinger solutions.
Abstract
In this work we shall review some of our recent results concerning unique continuation properties of solutions of Schr\"odinger equations. In this equations we include linear ones with a time depending potential and semi-linear ones.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Spectral Theory in Mathematical Physics · Mathematical Analysis and Transform Methods