An Elementary Proof of the Harnack Inequality for Non-Negative Infinity-Superharmonic Functions
| dc.contributor.author | Bhattacharya, Tilak | |
| dc.date.accessioned | 2020-06-10T21:09:21Z | |
| dc.date.available | 2020-06-10T21:09:21Z | |
| dc.date.issued | 2001-06-14 | |
| dc.description.abstract | We present an elementary proof of the Harnack inequality for non-negative viscosity supersolutions of Δ∞u = 0. This was originally proven by Lindqvist and Manfredi using sequences of solutions of the p-Laplacian. We work directly with the Δ∞ operator using the distance function as a test function. We also provide simple proofs of the Liouville property, Hopf boundary point lemma and Lipschitz continuity. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 8 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Bhattacharya, T. (2001). An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions. <i>Electronic Journal of Differential Equations, 2001</i>(44), pp. 1-8. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/11601 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Viscosity solutions | |
| dc.subject | Harnack inequality | |
| dc.subject | Infinite harmonic operator | |
| dc.subject | Distance function | |
| dc.title | An Elementary Proof of the Harnack Inequality for Non-Negative Infinity-Superharmonic Functions | |
| dc.type | Article |