# The spherical p-harmonic eigenvalue problem in non-smooth domains

Abstract : We prove the existence of p-harmonic functions under the form u(r, σ) = r −β ω(σ) in any cone C S generated by a spherical domain S and vanishing on ∂C S. We prove the uniqueness of the exponent β and of the normalized function ω under a Lipschitz condition on S.
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Journal articles

Cited literature [16 references]

https://hal.archives-ouvertes.fr/hal-01501604
Contributor : Laurent Veron <>
Submitted on : Tuesday, April 4, 2017 - 2:12:46 PM
Last modification on : Friday, February 19, 2021 - 4:10:02 PM
Long-term archiving on: : Wednesday, July 5, 2017 - 5:11:19 PM

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### Identifiers

• HAL Id : hal-01501604, version 1
• ARXIV : 1704.01037

### Citation

Konstantinos Gkikas, Laurent Véron. The spherical p-harmonic eigenvalue problem in non-smooth domains. Journal of Functional Analysis, Elsevier, 2018, 274, pp.1155-1176. ⟨hal-01501604⟩

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