Large‐Scale Analyticity and Unique Continuation for Periodic Elliptic Equations
Large‐Scale Analyticity and Unique Continuation for Periodic Elliptic Equations
复制标题
周期椭圆方程的大规模解析性和唯一延拓
DOI：
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发表时间：
2020
影响因子：
3
通讯作者：
Charles K. Smart
中科院分区：
文献类型：
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作者：
S. Armstrong;Tuomo Kuusi;Charles K. Smart
我们证明了具有周期系数的椭圆算子的解在大尺度上表现为具有周期修正的多项式逼近意义下的解析函数。等价地，与调和函数的经典估计一样，大尺度中的常数在k中指数地估计尺度，并且最小尺度在k中线性增长。因此，我们刻画了周期一致椭圆型方程的整体解，这些解对小δ| >； 0表现出类似于O(EXP(δ x| ))的增长。大规模解析性还意味着定量的唯一延拓结果，即具有最优误差项的三球定理以及在谱底部不存在L2特征函数的证明。©2020威利期刊有限责任公司。
We prove that a solution of an elliptic operator with periodic coefficients behaves on large scales like an analytic function in the sense of approximation by polynomials with periodic corrections. Equivalently, the constants in the large‐scale Ck, 1 estimate scale exponentially in k, just as for the classical estimate for harmonic functions, and the minimal scale grows at most linearly in k. As a consequence, we characterize entire solutions of periodic, uniformly elliptic equations that exhibit growth like O(exp(δ| x| )) for small δ > 0. The large‐scale analyticity also implies quantitative unique continuation results, namely a three‐ball theorem with an optimal error term as well as a proof of the nonexistence of L2 eigenfunctions at the bottom of the spectrum. © 2020 Wiley Periodicals LLC.
影响因子：
2
作者：
Kenig, Carlos;Zhu, Jiuyi
通讯作者：
Zhu, Jiuyi