Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 34 min ago
PreprintarXiv licencearXiv

Quantitative uniqueness for bi-Laplace equations with potentials

  • Long Teng
  • Zhiwei Wang
  • Jiuyi Zhu
Open at sourcePDFDOICite

Abstract

We study quantitative unique continuation for bi-Laplace equations Δ2u+V(x)u=0 by introducing some new weighted frequency functions. We establish quantitative three-ball inequalities and vanishing-order bounds for bounded and Hölder continuous potentials. Three-ball inequalities are built on rescaling invariant weighted frequency functions. The vanishing order results are shown by related, but different weighted frequency functions.

Related

  1. Quantitative uniqueness for bi-Laplace equations with C2 lower-order coefficients
    Zhiwei Wang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Sharp existence and non-existence for singular $1$-Laplace equations with Hardy potentials
    Juan Carlos Chata Ortiz, Francesco Petitta
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Uniqueness and Stability of Monge--Ampère Potentials in Big Cohomology Classes
    Quang-Tuan Dang, Lei Zhang, Bin Zhou
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Local and global C1,β-regularity for uniformly elliptic quasilinear equations of p-Laplace and Orlicz-Laplace type
    Carlo Alberto Antonini
    Nonlinear AnalysisPeer-reviewedCC BY18 citedGeneral mathematicsOpenAlex
  5. Uniqueness for the inverse Schrödinger problem in the plane with Lp potentials, p>1
    Cătălin I. Cârstea, Jenn-Nan Wang
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{teng2026quantitative,
  title = {{Quantitative uniqueness for bi-Laplace equations with potentials}},
  author = {Long Teng and Zhiwei Wang and Jiuyi Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.08866},
  eprint = {2608.08866},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.08866},
}
RIS
TY  - UNPB
TI  - Quantitative uniqueness for bi-Laplace equations with potentials
AU  - Long Teng
AU  - Zhiwei Wang
AU  - Jiuyi Zhu
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2608.08866
UR  - https://arxiv.org/abs/2608.08866
AB  - We study quantitative unique continuation for bi-Laplace equations Δ^2u+V(x)u=0 by introducing some new weighted frequency functions. We establish quantitative three-ball inequalities and vanishing-order bounds for bounded and Hölder continuous potentials. Three-ball inequalities are built on rescaling invariant weighted frequency functions. The vanishing order results are shown by related, but different weighted frequency functions.
ER  -