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

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
Journal	Mathematische Annalen
DOIs	https://doi.org/10.1007/s00208-020-02026-0
Publication status	Accepted/In press - 2020

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}",

year = "2020",

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

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AU - Davey, Blair

AU - Lin, Ching Lung

AU - Wang, Jenn Nan

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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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