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A sharp Trudinger-Moser type inequality in \(\mathbb R^2\). (English) Zbl 1300.35014

The authors establish a sharp Trudinger-Moser type inequality for a class of Schrödinger operators in \(\mathbb R^2\). It is obtained a result related to the compactness of the embedding of a subspace of \(W^{1,2}(\mathbb R^2)\) into the Orlicz space \(L_\Phi(\mathbb R^2)\) determined by \(\phi(t)=e^{\beta t^2}-1.\) It is proved the existence of an extremal function for this Trudinger-Moser inequality by performing a blow-up analysis.

MSC:

35J20 Variational methods for second-order elliptic equations
35J60 Nonlinear elliptic equations
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