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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

##### MSC:
 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
##### Keywords:
Trudinger’s inequality; uniqueness
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##### References:
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