ABSTRACT The Runge approximation is one of the interesting properties of partial differential equations. Studies have demonstrated its significance for sampling methods of inverse problems and learning‐based numerical methods for differential equations. In this paper, we discuss both qualitative and quantitative Runge approximation properties for the Lamé system. Our analysis relies on conditional stability of the Cauchy problem for the Lamé system and duality arguments, with optimal regularity conditions for the Lamé coefficients being taken into account. Under the fundamental assumption, the uniqueness result for the Cauchy problem leads to the qualitative Runge approximation property in the ‐norm. Under the strong assumption, employing the conditional stability estimates for the Cauchy problem and the truncated singular value decomposition, we derive quantitative Runge approximation estimates.
Li et al. (Sun,) studied this question.