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PreprintarXiv licencearXiv

Sharp Adams inequality for Critical Biharmonic Equations with Hardy--Hénon Weights in ℝ4

  • 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 ℝ4 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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Cite

BibTeXRIS
BibTeX
@misc{albuquerque2026sharp,
  title = {{Sharp Adams inequality for Critical Biharmonic Equations with Hardy--Hénon Weights in $\mathbbR^4$}},
  author = {J. C. de Albuquerque and J. Carvalho and L. M. Silva},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38078},
  eprint = {2610.38078},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38078},
}
RIS
TY  - UNPB
TI  - Sharp Adams inequality for Critical Biharmonic Equations with Hardy--Hénon Weights in ℝ^4
AU  - J. C. de Albuquerque
AU  - J. Carvalho
AU  - L. M. Silva
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.38078
UR  - https://arxiv.org/abs/2610.38078
AB  - We study a class of weighted fourth-order elliptic problems in 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.
ER  -