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math.AP2024
Dichotomy Results for the Electromagnetic Schrödinger Equation
Magdalena Czubak, Ian Miller, Svetlana Roudenko
The electromagnetic nonlinear Schrödinger (emNLS) equation is a variant of the well-studied nonlinear Schrödinger equation. In this article, we consider questions of global existen…
math.AP2024
The Meyers-Serrin theorem on Riemannian manifolds: a survey
Chi Hin Chan, Magdalena Czubak
We revisit the questions of density of smooth functions, and differential forms, in Sobolev spaces on Riemannian manifolds. We carefully show equivalence of weak covariant derivati…