On quantitative uniqueness for elliptic equations

Çamliyurt, Güher; Kukavica, Igor; Wang, Fei

doi:10.1007/s00209-018-2081-6

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2021

2022

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Cited by 3 publications

(2 citation statements)

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“…L ∞ ), which is, at least for complex valued coefficients, sharp [CKW1,CKW2]. Poon and Kurata showed that the frequency approach leads to unique continuation for p > n and q = ∞.…”

Section: Introductionmentioning

confidence: 98%

On quantitative uniqueness for parabolic equations

Kukavica¹,

Le²

2021

Preprint

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“…L ∞ ), which is, at least for complex valued coefficients, sharp [CKW1,CKW2]. Poon and Kurata showed that the frequency approach leads to unique continuation for p > n and q = ∞.…”

Section: Introductionmentioning

confidence: 98%

On quantitative uniqueness for parabolic equations

Kukavica¹,

Le²

2021

Preprint

Self Cite

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“…Such problems with Dirichlet boundary conditions have been extensively studied in the literature, c.f. [1,6,16,17,23]. However, there are very few results on Neumann or Robin problems.…”

Section: Introductionmentioning

confidence: 99%

Quantitative unique continuation for Robin boundary value problems on $C^{1,1}$ domains

Li¹,

Wang²

2021

Preprint

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In this paper, we prove two unique continuation results for second order elliptic equations with Robin boundary conditions on C 1,1 domains. We first prove a sharp vanishing order estimate of Robin problems with Lipschitz coefficients and differentiable potentials. This is comparable to the estimates for the interior case in [2, 24] and the Dirichlet case in [3]. Furthermore, it generalizes the result for the "Robin eigenfunctions" in [25], which dealt with the case with constant potentials. The second result in the current paper is the unique continuation from the boundary, which generalizes the one in [1] for Laplace equations with Neumann boundary conditions. Our result also improves [8] as we remove a geometric condition.

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On quantitative uniqueness for parabolic equations

Kukavica

2022

Journal of Differential Equations

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On quantitative uniqueness for elliptic equations

Cited by 3 publications

References 37 publications

On quantitative uniqueness for parabolic equations

On quantitative uniqueness for parabolic equations

Quantitative unique continuation for Robin boundary value problems on $C^{1,1}$ domains

On quantitative uniqueness for parabolic equations

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