Existence of solutions to a normalized F-infinity Laplacian equation
In this article, for a continuous function F that is twice differentiable at a point $x_0$, we define the normalized F-infinity Laplacian $\Delta_{F; \infty}^N$ which is a generalization of the usual normalized infinity Laplacian. Then for a bounded domain $\Omega\subset\mathbb{R}^n$, $f\in C(\...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/109/abstr.html |
| Summary: | In this article, for a continuous function F that is twice differentiable
at a point $x_0$, we define the normalized F-infinity Laplacian
$\Delta_{F; \infty}^N$ which is a generalization of the usual normalized
infinity Laplacian.
Then for a bounded domain $\Omega\subset\mathbb{R}^n$, $f\in C(\Omega)$ with
$\inf_\Omega f(x)>0$ and $g\in C(\partial\Omega)$, we obtain existence and
uniqueness of viscosity solutions to the Dirichlet boundary-value problem
$$\displaylines{
\Delta_{F; \infty}^N u=f, \quad \text{in }\Omega,\cr
u=g, \quad \text{on }\partial\Omega.
}$$ |
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| ISSN: | 1072-6691 |