A remark on C2 infinity-harmonic functions
| dc.contributor.author | Yu, Yifeng ( ) | |
| dc.date.accessioned | 2021-07-20T18:26:39Z | |
| dc.date.available | 2021-07-20T18:26:39Z | |
| dc.date.issued | 2006-10-06 | |
| dc.identifier.citation | Yu, Y. (2006). A remark on C2 infinity-harmonic functions. Electronic Journal of Differential Equations, 2006(122), pp. 1-4. | en_US |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://digital.library.txstate.edu/handle/10877/13995 | |
| dc.description.abstract | In this paper, we prove that any nonconstant, C2 solution of the infinity Laplacian equation uₓiuₓj uₓiₓj = 0 can not have interior critical points. This result was first proved by Aronsson [2] in two dimensions. When the solution is C4, Evans [6] established a Harnack inequality for |Du|, which implies that non-constant C4 solutions have no interior critical points for any dimension. Our method is strongly motivated by the work in [6]. | |
| dc.format | Text | |
| dc.format.extent | 4 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.language.iso | en | en_US |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | en_US |
| dc.source | Electronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Infinity Laplacian equation | en_US |
| dc.subject | Infinity harmonic function | en_US |
| dc.subject | Viscosity solutions | en_US |
| dc.title | A remark on C2 infinity-harmonic functions | en_US |
| dc.type | publishedVersion | |
| txstate.documenttype | Article | |
| dc.rights.license |  This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.description.department | Mathematics |
