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arXiv · 2002.07533

On removable singularities of solutions of higher order differential inequalities

A. A. Kon'kov·A. E. Shishkov
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Abstract

We obtain sufficient conditions for solutions of the $m$th-order differential inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, u) \ge f (x) g (|u|) \quad \mbox{in } B_1 \setminus \{ 0 \} $$ to have a removable singularity at zero, where $a_\alpha$, $f$, and $g$ are some functions, and $B_1 = \{ x : |x| < 1 \}$ is a unit ball in ${\mathbb R}^n$. Constructed examples demonstrate the exactness of these conditions.

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A. A. Kon'kov, A. E. Shishkov. 2020-02-18. On removable singularities of solutions of higher order differential inequalities. https://arxiv.org/abs/2002.07533

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