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<p>We consider a strong unique continuation property for the fourth order elliptic equation involving singular potential on the Heisenberg group by way of the argument of Almgren frequency function. By splitting it into the system with two elliptic equations of second order, we prove our main result based on the monotonicity property of frequency function and doubling condition of solutions, which is gotten by some local version of the Hardy-Rellich type inequality with boundary term and interior Caccioppoli type inequality.</p>

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Strong unique continuation for fourth order elliptic equations on the Heisenberg group

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Yurui Ma,
  • Shenzhou Zheng

摘要

We consider a strong unique continuation property for the fourth order elliptic equation involving singular potential on the Heisenberg group by way of the argument of Almgren frequency function. By splitting it into the system with two elliptic equations of second order, we prove our main result based on the monotonicity property of frequency function and doubling condition of solutions, which is gotten by some local version of the Hardy-Rellich type inequality with boundary term and interior Caccioppoli type inequality.