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Quantitative uniqueness for bi-Laplace equations with C2 lower-order coefficients

  • Zhiwei Wang
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Abstract

We study quantitative unique continuation for bi-Laplace equations Δ2u+W(x)Δu+V(x)·∇ u=0 with C2 lower-order coefficients. Using the weighted-frequency function, we establish an L∞ three-ball inequality whose exponential factor has coefficient dependence |W|C21/2+|V|C21/3. Under some normalization, we obtain a vanishing-order bound of size C(|W|C21/2+|V|C21/3).

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Cite

BibTeXRIS
BibTeX
@misc{wang2026quantitative,
  title = {{Quantitative uniqueness for bi-Laplace equations with $C^2$ lower-order coefficients}},
  author = {Zhiwei Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03614},
  eprint = {2610.03614},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03614},
}
RIS
TY  - UNPB
TI  - Quantitative uniqueness for bi-Laplace equations with C^2 lower-order coefficients
AU  - Zhiwei Wang
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03614
UR  - https://arxiv.org/abs/2610.03614
AB  - We study quantitative unique continuation for bi-Laplace equations Δ^2u+W(x)Δu+V(x)·∇ u=0 with C^2 lower-order coefficients. Using the weighted-frequency function, we establish an L^∞ three-ball inequality whose exponential factor has coefficient dependence |W|_C^2^1/2+|V|_C^2^1/3. Under some normalization, we obtain a vanishing-order bound of size C(|W|_C^2^1/2+|V|_C^2^1/3).
ER  -