Strong unique continuation for the Lamé system with less regular coefficients

Blair Davey; Ching Lung Lin; Jenn Nan Wang

doi:10.1007/s00208-020-02026-0

Strong unique continuation for the Lamé system with less regular coefficients

Blair Davey, Ching Lung Lin, Jenn Nan Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study the strong unique continuation property (SUCP) for the Lamé system in the plane. The main contribution of our work is to prove that the SUCP holds when Lamé coefficients (μ, λ) ∈ W²^,^s(Ω) × L^∞(Ω) for some s> 4 / 3. In other words, we establish the SUCP for the Lamé system in the plane when λ is bounded and μ belongs to certain Hölder classes.

Original language	English
Pages (from-to)	1005-1029
Number of pages	25
Journal	Mathematische Annalen
Volume	381
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-020-02026-0
Publication status	Published - 2021 Oct

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1007/s00208-020-02026-0

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title = "Strong unique continuation for the Lam{\'e} system with less regular coefficients",

abstract = "We study the strong unique continuation property (SUCP) for the Lam{\'e} system in the plane. The main contribution of our work is to prove that the SUCP holds when Lam{\'e} coefficients (μ, λ) ∈ W2,s(Ω) × L∞(Ω) for some s> 4 / 3. In other words, we establish the SUCP for the Lam{\'e} system in the plane when λ is bounded and μ belongs to certain H{\"o}lder classes.",

author = "Blair Davey and Lin, {Ching Lung} and Wang, {Jenn Nan}",

note = "Funding Information: Part of this research was carried out while the first author was visiting the National Center for Theoretical Sciences (NCTS) at National Taiwan University. The first author wishes to thank the NCTS for their financial support and their kind hospitality during her visit to Taiwan. Funding Information: Davey is supported in part by the Simons Foundation Grant number 430198. Lin is partially supported by the Ministry of Science and Technology of Taiwan. Wang is supported in part by the Ministry of Science and Technology, Taiwan (MOST 108-2115-M-002-002-MY3). Funding Information: Part of this research was carried out while the first author was visiting the National Center for Theoretical Sciences (NCTS) at National Taiwan University. The first author wishes to thank the NCTS for their financial support and their kind hospitality during her visit to Taiwan. Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2021",

month = oct,

doi = "10.1007/s00208-020-02026-0",

language = "English",

volume = "381",

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TY - JOUR

T1 - Strong unique continuation for the Lamé system with less regular coefficients

AU - Davey, Blair

AU - Lin, Ching Lung

AU - Wang, Jenn Nan

N1 - Funding Information: Part of this research was carried out while the first author was visiting the National Center for Theoretical Sciences (NCTS) at National Taiwan University. The first author wishes to thank the NCTS for their financial support and their kind hospitality during her visit to Taiwan. Funding Information: Davey is supported in part by the Simons Foundation Grant number 430198. Lin is partially supported by the Ministry of Science and Technology of Taiwan. Wang is supported in part by the Ministry of Science and Technology, Taiwan (MOST 108-2115-M-002-002-MY3). Funding Information: Part of this research was carried out while the first author was visiting the National Center for Theoretical Sciences (NCTS) at National Taiwan University. The first author wishes to thank the NCTS for their financial support and their kind hospitality during her visit to Taiwan. Publisher Copyright: © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2021/10

Y1 - 2021/10

N2 - We study the strong unique continuation property (SUCP) for the Lamé system in the plane. The main contribution of our work is to prove that the SUCP holds when Lamé coefficients (μ, λ) ∈ W2,s(Ω) × L∞(Ω) for some s> 4 / 3. In other words, we establish the SUCP for the Lamé system in the plane when λ is bounded and μ belongs to certain Hölder classes.

AB - We study the strong unique continuation property (SUCP) for the Lamé system in the plane. The main contribution of our work is to prove that the SUCP holds when Lamé coefficients (μ, λ) ∈ W2,s(Ω) × L∞(Ω) for some s> 4 / 3. In other words, we establish the SUCP for the Lamé system in the plane when λ is bounded and μ belongs to certain Hölder classes.

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SN - 0025-5831

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ER -

Strong unique continuation for the Lamé system with less regular coefficients

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