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

Ogawa, Takayoshi

Nonlinear Anal., Theory Methods Appl. 14, No. 9, 765-769 (1990).

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

References:

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