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arXiv · 1505.00254

Pointwise Bounds and Blow-up for Nonlinear Polyharmonic Inequalities

Steven D. Taliaferro
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Abstract

We obtain results for the following question where $m\ge 1$ and $n\ge 2$ are integers. Question. For which continuous functions $f\colon [0,\infty)\to [0,\infty)$ does there exist a continuous function $\varphi\colon (0,1)\to (0,\infty)$ such that every $C^{2m}$ nonnegative solution $u(x)$ of $ 0 \le -\Delta^m u\le f(u)\quad$ in $B_2(0)\setminus\{0\}\subset {\bf R}^n $ satisfies $u(x) = O(\varphi(|x|))\quad \text{as } x\to 0 $ and what is the optimal such $\varphi$ when one exists?

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Steven D. Taliaferro. 2015-05-01. Pointwise Bounds and Blow-up for Nonlinear Polyharmonic Inequalities. https://doi.org/10.1016/j.anihpc.2012.12.011

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