Abstract
This paper deals with an improvement of the Trudinger–Moser inequality for the Sobolev space W1,N(Ω) involving domains of the type Ω=RN−1×(a,b), where N≥2 and a<b. As an application of this result and by using minimax methods, we establish sufficient conditions for the existence of solutions for a class of elliptic problems with Neumann boundary conditions and nonlinearities with critical exponential growth.
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