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dc.contributor.authorLe, An ( )
dc.date.accessioned2021-07-20T16:19:51Z
dc.date.available2021-07-20T16:19:51Z
dc.date.issued2006-09-18
dc.identifier.citationLê, A. (2006). On the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacian. Electronic Journal of Differential Equations, 2006(111), pp. 1-9.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13984
dc.description.abstractLet Λpp be the best Sobolev embedding constant of W1,p(Ω) ↪ Lp(∂Ω), where Ω is a smooth bounded domain in ℝN. We prove that as p → ∞ the sequence Λp converges to a constant independent of the shape and the volume of Ω, namely 1. Moreover, for any sequence of eigenfunctions up (associated with Λp), normalized by ∥upL∞(∂Ω) = 1, there is a subsequence converging to a limit function u which satisfies, in the viscosity sense, an ∞-Laplacian equation with a boundary condition.
dc.formatText
dc.format.extent9 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectNonlinear elliptic equationsen_US
dc.subjectEigenvalue problemsen_US
dc.subjectp-Laplacianen_US
dc.subjectNonlinear boundary conditionen_US
dc.subjectSteklov problemen_US
dc.subjectViscosity solutionsen_US
dc.titleOn the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacianen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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