Non-polynomial entire solutions to $\sigma_{k}$ equations

arxiv: 1503.06843 · v2 · pith:M5YYGXYMnew · submitted 2015-03-23 · 🧮 math.AP

Non-polynomial entire solutions to σ_(k) equations

Micah Warren This is my paper

classification 🧮 math.AP

keywords non-polynomialsigmasolutionsentireequationequationsexhibithessian

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For $2k \leq n+1$, we exhibit non-polynomial solutions to the Hessian equation \[ \sigma_{k}(D^{2}u)=1 \] on all of $\mathbb{R}^{n}.$

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