Sharp Adams inequality for Critical Biharmonic Equations with Hardy--Hénon Weights in $\mathbb{R}^4$

J. C. de Albuquerque; J. Carvalho; L. M. Silva

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arXiv · 2610.38078

Sharp Adams inequality for Critical Biharmonic Equations with Hardy--Hénon Weights in $\mathbb{R}^4$

J. C. de Albuquerque·J. Carvalho·L. M. Silva

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Abstract

We study a class of weighted fourth-order elliptic problems in $\mathbb{R}^4$ driven by the biharmonic operator and involving Hardy--Hénon type potentials. The nonlinear term has critical exponential growth in the sense of an Adams-type inequality. The weights $|x|^a$ and $|x|^b$ allow us to incorporate singular, vanishing, and unbounded effects in a unified variational framework. We introduce a suitable weighted function space, establish Sobolev-type embeddings, and prove an Adams-type inequality adapted to this setting. Under appropriate structural assumptions on the nonlinearity, we prove the existence of nontrivial weak solutions. We also obtain regularity properties and derive a Pohozaev identity, which leads to a nonexistence result.

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BibTeX RIS

J. C. de Albuquerque, J. Carvalho, L. M. Silva. 2026-10-27. Sharp Adams inequality for Critical Biharmonic Equations with Hardy--Hénon Weights in $\mathbb{R}^4$. https://arxiv.org/abs/2610.38078

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