On the embedding of weighted Sobolev spaces with applications to a planar nonlinear Schrödinger equation

2024/12/13 by Azzolini, Antonio, Pomponio, Alessio, Secchi, Simone
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.10067

Abstract

In this paper we study the embedding properties for the weighted Sobolev space H¹_V(ℝ^N) into the Lebesgue weighted space L^τ_W(ℝ^N). Here V and W are diverging weight functions. The different behaviour of V with respect to W at infinity plays a crucial role. Particular attention is paid to the case V=W. This situation is very delicate since it depends strongly on the dimension and, in particular, N=2 is somewhat a limit case. As an application, an existence result for a planar nonlinear Schrödinger equation in presence of coercive potentials is provided.

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