Quantitative uniqueness of solutions to second-order elliptic equations with singular lower order terms
Quantitative uniqueness of solutions to second-order elliptic equations with singular lower order terms
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DOI：
10.1080/03605302.2019.1629957
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发表时间：
2017-02
影响因子：
1.9
通讯作者：
Blair Davey;Jiuyi Zhu
中科院分区：
文献类型：
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作者：
Blair Davey;Jiuyi Zhu
摘要本文研究了具有奇异低阶项的二阶椭圆方程解的一些定量唯一连续性质。首先，我们通过估计解的最大消失阶来量化强唯一连续性质。也就是说，当u是某个开的连通子集中的非平凡解时，我们用V和W在它们各自的勒贝格空间中的范数来刻画解的消失序。然后，利用这些最大阶消失估计，我们建立了解在无穷远处的唯一连续的定量结果。我们工作中的主要工具是关于p和q值范围的Carleman估计的新版本。
Abstract In this article, we study some quantitative unique continuation properties of solutions to second-order elliptic equations with singular lower order terms. First, we quantify the strong unique continuation property by estimating the maximal vanishing order of solutions. That is, when u is a nontrivial solution to in some open, connected subset of where we characterize the vanishing order of solutions in terms of the norms of V and W in their respective Lebesgue spaces. Then, using these maximal order of vanishing estimates, we establish quantitative unique continuation at infinity results for solutions to in The main tools in our work are new versions of Carleman estimates for a range of p and q values.