On the Properties of Infinity-Harmonic Functions and an Application to Capacitary Convex Rings
| dc.contributor.author | Bhattacharya, Tilak | |
| dc.date.accessioned | 2020-09-10T17:40:22Z | |
| dc.date.available | 2020-09-10T17:40:22Z | |
| dc.date.issued | 2002-11-28 | |
| dc.description.abstract | We study positive ∞-harmonic functions in bounded domains. We use the theory of viscosity solutions in this work. We prove a boundary Harnack inequality and a comparison result for such functions near a flat portion of the boundary where they vanish. We also study ∞-capacitary functions on convex rings. We show that the gradient satisfies a global maximum principle, it is nonvanishing outside a set of measure zero and the level sets are star-shaped. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Bhattacharya, T. (2002). On the properties of infinity-harmonic functions and an application to capacitary convex rings. <i>Electronic Journal of Differential Equations, 2002</i>(101), pp. 1-22. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12565 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, 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, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Viscosity solutions | |
| dc.subject | Boundary Harnack inequality | |
| dc.subject | Infinity-Laplacian | |
| dc.subject | Capacitary functions | |
| dc.subject | Convex rings | |
| dc.title | On the Properties of Infinity-Harmonic Functions and an Application to Capacitary Convex Rings | |
| dc.type | Article |