In this paper we prove strong unique continuation principle and unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the Caffarelli-Silvestre extension method combined with an Almgren type monotonicity formula. The corresponding extended problem is formulated as a systems of two second order equations with singular or degenerate weights in a half-space, for which asymptotics estimates are derived by a blow-up analysis.

中文翻译：

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高阶分数拉普拉斯方程的独特延拓原理

在本文中，我们从开放域中高阶分数拉普拉斯方程的解的正测度集证明了强大的唯一延拓原理和唯一延拓。我们的证明基于 Caffarelli-Silvestre 扩展方法结合 Almgren 类型单调性公式。相应的扩展问题被表述为在半空间中具有奇异权重或退化权重的两个二阶方程的系统，其渐近估计是通过爆炸分析得出的。