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EnglishWe prove existence and uniqueness of classical solutions of the anisotropic prescribed mean curvature problem egin{equation*} { m -div}left({ abla u}/{sqrt{1 + | abla u|^2}} ight) = -au + {b}/{sqrt{1 + | abla u|^2}}, ext{ in } B, quad u=0, ext{ on } partial B, end{equation*} where $a,b>0$ are given parameters and $B$ is a ball in ${mathbb R}^N$. The solution we find is positive, radially symmetric, radially decreasing and concave. This equation has been proposed as a model of the corneal shape in the recent papers [13,14,15,18,17], where however a linearized version of the equation has been investigated.
| Titolo: | Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape |
| Autori: | OMARI, PIERPAOLO (Corresponding) |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| Abstract: | We prove existence and uniqueness of classical solutions of the anisotropic prescribed mean curvature problem egin{equation*} { m -div}left({ abla u}/{sqrt{1 + | abla u|^2}} ight) = -au + {b}/{sqrt{1 + | abla u|^2}}, ext{ in } B, quad u=0, ext{ on } partial B, end{equation*} where $a,b>0$ are given parameters and $B$ is a ball in ${mathbb R}^N$. The solution we find is positive, radially symmetric, radially decreasing and concave. This equation has been proposed as a model of the corneal shape in the recent papers [13,14,15,18,17], where however a linearized version of the equation has been investigated. |
| Handle: | http://hdl.handle.net/11368/2922393 |
| ISBN: | 1-60133-018-9 |
| URL: | http://www.aimsciences.org/article/doi/10.3934/proc.2015.0297 |
| Appare nelle tipologie: | 4.1 Contributo in Atti Convegno (Proceeding) |
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