On a weighted Sobolev embedding on the upper half-space in a borderline case

Abreu, Emerson; Medeiros, Everaldo S.; Yang, Jiachao

doi:10.1007/s10231-022-01217-7

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Weighted Sobolev Embedding1

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2023

2024

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Cited by 2 publications

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“…In this section we will prove theorem 1.1. In our proof we borrow some of the ideas from the recent article [1].…”

Section: Weighted Sobolev Embeddingmentioning

confidence: 99%

Nonlinear divergence equation with potentials vanishing in some direction at infinity: the exponential critical case

Cardoso,

Carvalho,

de Medeiros

2024

Nonlinearity

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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 ) in R 2 , where the nonlinearity f has exponential critical growth in sense of Trudinger–Moser.

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“…In this section we will prove theorem 1.1. In our proof we borrow some of the ideas from the recent article [1].…”

Section: Weighted Sobolev Embeddingmentioning

confidence: 99%