REMOVABLE SETS FOR NONLINEAR WAVE EQUATIONS IN TERMS OF HAUSDORFF MEASURES

Abstract

We prove Radó theorem for nonlinear wave equations. Considering $u$ as a locally Lipschitz continuous function on an open set $\mathcal{X}$ in $\mathbb{R}^{n+1}$ to be a weak solution of the equations $ \partial_{tt}u-div(|u’|^{p-2}u’)=0$, on $\mathcal{X}\backslash u^{-1}(0)$, where $p \ge 2$, and employing the Hausdorff measure, we show that $u$ is a weak solution of these nonlinear wave equations in the entire $\mathcal{X}.$