Work

Schwartz very weak solutions for Schrödinger type equations with distributional coefficients

Year: 2025

Type: article

Abstract: This paper continues the analysis of Schrödinger type equations with distributional coefficients initiated by the authors in a recent paper in Journal of Differential Equations (425) 2025. Here, we consider coefficients that are tempered distributions with respect to the space variable and are continuous in time. We prove that the corresponding Cauchy problem, which in general cannot even be stated in the standard distributional setting, admits a Schwartz very weak solution which is unique modulo negligible perturbations. Consistency with the classical theory is proved in the case of regular coefficients and Schwartz Cauchy data.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2025.10077

Authors: Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello, Claudia Garetto

Institutions: Universidade de São Paulo, University of Ferrara, University of Turin, Queen Mary University of London

Language: English

Topic: Mathematical and Theoretical Analysis

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Fundação de Amparo à Pesquisa do Estado de São Paulo, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Engineering and Physical Sciences Research Council