Weyl-type eigenvalue bounds for the fractional p-Laplacian

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dc.authorid0000-0002-9080-4242
dc.contributor.authorHasanov, Mahir
dc.date.accessioned2026-01-31T15:08:48Z
dc.date.available2026-01-31T15:08:48Z
dc.date.issued2025
dc.departmentİstanbul Beykent Üniversitesi
dc.description.abstractIn this paper we study Weyl-type eigenvalue bounds for the variational eigenvalues of the fractional p-Laplacian on a bounded domain Omega subset of Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega \subset \mathbb{R}<^>{n}$\end{document} with a Lipschitz boundary. We prove that lambda m(Omega)>= C|Omega|-spnmspn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda _{m}(\Omega )\geq C |\Omega |<^>{-\frac{sp}{n}} m<^>{\frac{sp}{n}}$\end{document}, where C=C(s,p,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C=C(s,p,n)$\end{document}. This result partially confirms a conjecture of Iannizzotto and Squassina (Asymptot. Anal. 88: 233-245, 2014). We also study the auxiliary weighted eigenvalue problem (1.2) and obtain that lambda m(w,Omega)>= C(integral Omega wr(x)dx)-1r|Omega|1r-spnmspn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda _{m}(w, \Omega )\geq C\Bigl(\int _{\Omega }w<^>{r}(x)dx \Bigr)<^>{-\frac{1}{r}}| \Omega |<^>{\frac{1}{r}-\frac{sp}{n}} m<^>{\frac{sp}{n}}$\end{document}, where C=C(s,p,n,r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C=C(s,p,n,r)$\end{document}. The main method used in this paper is the approximation method developed by Birman and Solomyak (Quantitative Analysis in Sobolev Imbedding Theorems and Applications to Spectral Theory, 1980).
dc.identifier.doi10.1186/s13661-025-02094-8
dc.identifier.issn1687-2770
dc.identifier.issue1
dc.identifier.scopus2-s2.0-105010437784
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org./10.1186/s13661-025-02094-8
dc.identifier.urihttps://hdl.handle.net/20.500.12662/10761
dc.identifier.volume2025
dc.identifier.wosWOS:001525624600001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofBoundary Value Problems
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260128
dc.subjectFractional p-Laplacian
dc.subjectEigenvalue
dc.subjectApproximation method
dc.subjectEigenvalue bounds
dc.titleWeyl-type eigenvalue bounds for the fractional p-Laplacian
dc.typeArticle

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