Unique Continuation on Quadratic Curves for Harmonic Functions
Yufei Ke, Yu Chen
TL;DR
This paper investigates the unique continuation property of harmonic functions along quadratic curves, employing complex extension methods, and provides numerical algorithms with stability estimates demonstrated through examples.
Contribution
It introduces a novel approach using complex extension for unique continuation along quadratic curves and develops a numerical algorithm with stability analysis.
Findings
Stability estimates for harmonic functions on quadratic curves are established.
Numerical algorithms based on collocation and Tikhonov regularization are effective.
The method applies to parabolic and hyperbolic curves with demonstrated examples.
Abstract
The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated. The numerical algorithm is provided based on collocation method and Tikhonov regularization. The stability estimates on parabolic and hyperbolic curves for harmonic functions are demonstrated by numerical examples respectively.
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Taxonomy
TopicsNumerical methods in inverse problems · Image and Signal Denoising Methods · Stability and Controllability of Differential Equations