A proof of Trudinger’s inequality and its application to nonlinear Schrödinger equations. (English) Zbl 0715.35073

The author gives a new proof of a version of Trudinger’s inequality for unbounded domains in \({\mathbb{R}}^ 2\). This proof uses the properties of the free Schrödinger propagator. The obtained inequality is applied to prove the uniqueness of weak solutions to nonlinear Schrödinger equations.
Reviewer: C.Popa


35Q55 NLS equations (nonlinear Schrödinger equations)
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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