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- W4386875391 abstract "In this paper, we prove the strong unique continuation property for the following fourth order degenerate elliptic equation begin{equation*} Delta^2_{X}u=Vu, end{equation*} where $Delta_{X}=Delta_{x}+|x|^{2alpha}Delta_{y}$ ($0<alphaleq1$), with $xinmathbb{R}^{m}, yinmathbb{R}^{n}$, denotes the Baouendi-Grushin type subelliptic operators, and the potential $V$ satisfies the strongly singular growth assumption $|V|leq frac{c_0}{rho^4}$, where begin{equation*} rho=left(|x|^{2(alpha+1)}+(alpha+1)^2|y|^2right)^{frac{1}{2(alpha+1)}} end{equation*} is the gauge norm. The main argument is to introduce an Almgren's type frequency function for the solutions, and show its monotonicity to obtain a doubling estimate based on setting up some refined Hardy-Rellich type inequalities on the gauge balls with boundary terms." @default.
- W4386875391 created "2023-09-20" @default.
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- W4386875391 date "2023-09-17" @default.
- W4386875391 modified "2023-09-27" @default.
- W4386875391 title "Strong unique continuation property for fourth order Baouendi-Grushin type subelliptic operators with strongly singular potential" @default.
- W4386875391 doi "https://doi.org/10.48550/arxiv.2309.09172" @default.
- W4386875391 hasPublicationYear "2023" @default.
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