existence of solutions to a normalized f-infinity laplacian equation
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ID: 183765
2014
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Abstract
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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| Reference Key |
wang2014electronicexistence
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|---|---|
| Authors | ;Hua Wang;Yijun He |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2014 |
| DOI |
DOI not found
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| URL | |
| Keywords | Keywords not found |
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