Article contents
LYAPUNOV-TYPE INEQUALITY FOR EXTREMAL PUCCI’S EQUATIONS
Published online by Cambridge University Press: 29 January 2020
Abstract
In this article, we establish a Lyapunov-type inequality for the following extremal Pucci’s equation: $$\begin{eqnarray}\left\{\begin{array}{@{}ll@{}}{\mathcal{M}}_{\unicode[STIX]{x1D706},\unicode[STIX]{x1D6EC}}^{+}(D^{2}u)+b(x)|Du|+a(x)u=0 & \text{in}~\unicode[STIX]{x1D6FA},\\ u=0 & \text{on}~\unicode[STIX]{x2202}\unicode[STIX]{x1D6FA},\end{array}\right.\end{eqnarray}$$
$\unicode[STIX]{x1D6FA}$ is a smooth bounded domain in
$\mathbb{R}^{N}$,
$N\geq 2$. This work generalizes the well-known works on the Lyapunov inequality for extremal Pucci’s equations with gradient nonlinearity.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 109 , Issue 3 , December 2020 , pp. 416 - 430
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
Footnotes
Communicated by J. McCoy
References
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