关于Cayley Heisenberg群上次椭圆p-Laplace算子的唯一延拓性

doi:10.12677/pm.2026.168187

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关于Cayley Heisenberg群上次椭圆p-Laplace算子的唯一延拓性
The Unique Continuation Property for the p-Subelliptic-Laplace Operator on the Cayley Heisenberg Group

DOI: 10.12677/pm.2026.168187, PDF, 科研立项经费支持
作者: 刘慧萍, 廖冬妮^*：赣南师范大学数学与计算机科学学院，江西赣州
关键词: Cayley Heisenberg群；次椭圆p-Laplace方程；频率函数；唯一延拓性；Cayley Heisenberg Group； p-Sub-Laplace Equation； Frequency Function； Unique Continuation Property

摘要: 本文的主要目标是建立Cayley Heisenberg群

C ℋ^{n}

上次椭圆p-Laplace方程的解的唯一延拓性，通过引入Almgren函数并研究其相关性质，在频率函数局部有界的假设下，建立能量积分的二重性，进而得到次椭圆p-Laplace方程的弱解的唯一延拓性。

Abstract: The main purpose of this paper is to establish the unique continuation property of solutions to the p-subelliptic-Laplace equation on Cayley Heisenberg group. By introducing the Almgren function and presenting its relevant properties, a doubling estimate for the energy integral is established under the assumption that the frequency function is locally bounded, thereby establishing the unique continuation property of weak solutions to the p-subelliptic-Laplace equation.

文章引用：刘慧萍, 廖冬妮. 关于Cayley Heisenberg群上次椭圆p-Laplace算子的唯一延拓性[J]. 理论数学, 2026, 16(8): 131-146. https://doi.org/10.12677/pm.2026.168187

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