Abstract

The purpose of this article is to state some weighted Sobolev embedding involving functions that vanishing only in a direction. In this setting we prove a weighted Trudinger–Moser type inequality and as an application, we addressed the existence of solutions to a class of elliptic equation of the form −div(a(x)∇u)+V(x)u=K(x)f(u)inR2, where the nonlinearity f has exponential critical growth in sense of Trudinger–Moser.

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