REMOVABLE SETS FOR THE WAVE EQUATIONS IN TERMS OF HAUSDORFF MEASURE
Keywords:
hyperbolic equations, removable sets, Hausdorff measureDOI:
https://doi.org/10.17654/0975045225004Abstract
We prove a Radó theorem for the wave equations. Namely, we consider $u$ to be a locally Lipschitz continuous function on an open set $\mathcal{X} \in \mathbb{R}^{n+1}$ and weakly solution to the wave equations $\partial_{t t} u-\operatorname{div}(\nabla u)=0$ away from the zero set $u^{-1}(0)$ in $\mathcal{X}$. We prove that $u$ is a weak solution to these wave equations in all of $\mathcal{X}$.
Received: October 15, 2024
Accepted: December 7, 2024
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