Work

On a supercritical Hardy–Sobolev type inequality with logarithmic term and related extremal problem

Year: 2024

Type: article

Abstract: Our main goal is to investigate supercritical Hardy–Sobolev type inequalities with a logarithmic term and their corresponding variational problem. We prove the existence of extremal functions for the associated variational problem, despite the loss of compactness. As an application, we show the existence of weak solution to a general class of related elliptic partial differential equations with a logarithmic term.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ada1c0

Authors: José Francisco de Oliveira, Jeferson Silva

Institutions: Universidade Federal do Piauí, Universidade Federal do Delta do Parnaíba

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico

Awards: G6474521095, G7913905087