On the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacian
| dc.contributor.author | Le, An | |
| dc.date.accessioned | 2021-07-20T16:19:51Z | |
| dc.date.available | 2021-07-20T16:19:51Z | |
| dc.date.issued | 2006-09-18 | |
| dc.description.abstract | Let Λp p 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 ∥up∥L∞(∂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.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 9 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Lê, A. (2006). On the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacian. <i>Electronic Journal of Differential Equations, 2006</i>(111), pp. 1-9. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13984 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Nonlinear elliptic equations | |
| dc.subject | Eigenvalue problems | |
| dc.subject | p-Laplacian | |
| dc.subject | Nonlinear boundary condition | |
| dc.subject | Steklov problem | |
| dc.subject | Viscosity solutions | |
| dc.title | On the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacian | |
| dc.type | Article |