On removable singularities of solutions of higher order differential inequalities

2020/02/18 by Kon'kov, A. A., Shishkov, A. E.
#35B33 #35B38 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.07533

Abstract

We obtain sufficient conditions for solutions of the mth-order differential inequality ∑_{|α| = m} ∂^αa_α(x, u) ≥ f (x) g (|u|) in B₁ ∖ \ 0 \ to have a removable singularity at zero, where a_α, f, and g are some functions, and B₁ = \ x : |x| < 1 \ is a unit ball in \mathbb Rⁿ. Constructed examples demonstrate the exactness of these conditions.

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