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Adams-Onofri Inequality with Logarithmic Weight and the Associated Mean Field Bi-Harmonic Equation

Adams-Onofri Inequality with Logarithmic Weight and the Associated Mean Field Bi-Harmonic Equation

Year:    2024

Author:    Pan Ma, Maochun Zhu

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 417–426

Abstract

This paper is devoted to establishing the Adams-Onofri inequality with logarithmic weight for the second order radial Sobolev space defined on the unit ball in $\mathbb{R}^4.$ By using this inequality we obtain the existence of solutions for mean field biharmonic equation with logarithmic weight.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v37.n4.4

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 417–426

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Adams-Onofri inequality Logarithmic weight mean field equation existence.

Author Details

Pan Ma

Maochun Zhu