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Volume 37, Issue 4
Adams-Onofri Inequality with Logarithmic Weight and the Associated Mean Field Bi-Harmonic Equation

Pan Ma & Maochun Zhu

DOI: 10.4208/jpde.v37.n4.4

J. Part. Diff. Eq., 37 (2024), pp. 417-426.

Published online: 2024-12

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  • 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.

  • Keywords

Adams-Onofri inequality, Logarithmic weight, mean field equation, existence.

  • AMS Subject Headings

46E35, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-37-417, author = {Ma , Pan and Zhu , Maochun}, title = {Adams-Onofri Inequality with Logarithmic Weight and the Associated Mean Field Bi-Harmonic Equation}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {4}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/23689.html} }
TY - JOUR T1 - Adams-Onofri Inequality with Logarithmic Weight and the Associated Mean Field Bi-Harmonic Equation AU - Ma , Pan AU - Zhu , Maochun JO - Journal of Partial Differential Equations VL - 4 SP - 417 EP - 426 PY - 2024 DA - 2024/12 SN - 37 DO - http://doi.org/10.4208/jpde.v37.n4.4 UR - https://global-sci.org/intro/article_detail/jpde/23689.html KW - Adams-Onofri inequality, Logarithmic weight, mean field equation, existence. AB -

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.

Ma , Pan and Zhu , Maochun. (2024). Adams-Onofri Inequality with Logarithmic Weight and the Associated Mean Field Bi-Harmonic Equation. Journal of Partial Differential Equations. 37 (4). 417-426. doi:10.4208/jpde.v37.n4.4
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