Doubling properties of caloric functions

Escauriaza, Luis; Fernández, Francisco Javier; Vessella, Sergio

doi:10.1080/00036810500277082

Cited by 90 publications

(83 citation statements)

References 19 publications

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“…We will use the doubling property of u(·, 0) proved by Escauriaza, Fernández and Vessella [2]. We present their arguments here in the form that we need.…”

Section: First Stepmentioning

confidence: 99%

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On a question of Landis and Oleinik

Nguyen

2010

Trans. Amer. Math. Soc.

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“…We will use the doubling property of u(·, 0) proved by Escauriaza, Fernández and Vessella [2]. We present their arguments here in the form that we need.…”

Section: First Stepmentioning

confidence: 99%

“…To prove this, we first adapt arguments of [2] and [9] to show that there exists s > 0, such that for small t, we have…”

Section: Proposition 23 Suppose That U Is As In the Hypothesis Of Tmentioning

confidence: 99%

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On a question of Landis and Oleinik

Nguyen

2010

Trans. Amer. Math. Soc.

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“…The first one, Lemma 1, is in a certain sense a localized version of the standard energy inequality satisfied by solutions of parabolic inequalities (See [7,Lemmas 1 and 5] for other versions of this Lemma). The Lemmas 2 and 3 appeared in [7,Lemmas 2,3].…”

Section: First Proof Of Theoremmentioning

confidence: 99%

Decay at infinity of caloric functions within characteristic hyperplanes

Escauriaza

Kenig

Ponce

et al. 2006

Mathematical Research Letters

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“…The main idea to prove Proposition 2.1 originates from the papers [7,2]. We begin with introducing a technical lemma, which is the base of the proof to Proposition 2.1.…”

Section: Proof Of Proposition 21mentioning

confidence: 99%

Quantitative unique continuation for the semilinear heat equation in a convex domain

Phung

Wang

2010

Journal of Functional Analysis

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In this paper, we study certain unique continuation properties for solutions of the semilinear heat equation ∂ t u − u = g(u), with the homogeneous Dirichlet boundary condition, over Ω × (0, T * ). Ω is a bounded, convex open subset of R d , with a smooth boundary for the subset. The function g : R → R satisfies certain conditions. We establish some observation estimates for (u − v), where u and v are two solutions to the above-mentioned equation. The observation is made over ω × {T }, where ω is any non-empty open subset of Ω, and T is a positive number such that both u and v exist on the interval [0, T ]. At least two results can be derived from these estimates: (i) if (u − v)(·, T ) L 2 (ω) = δ, then (u − v)(·, T ) L 2 (Ω) Cδ α where constants C > 0 and α ∈ (0, 1) can be independent of u and v in certain cases; (ii) if two solutions of the above equation hold the same value over ω × {T }, then they coincide over Ω × [0, T m ). T m indicates the maximum number such that these two solutions exist on [0, T m ).

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Doubling properties of caloric functions

Abstract: Abstract. We obtain quantitative estimates of unique continuation for solutions to parabolic equations: doubling properties and two-sphere one-cylinder inequalities.

Cited by 90 publications

References 19 publications

On a question of Landis and Oleinik

On a question of Landis and Oleinik

Decay at infinity of caloric functions within characteristic hyperplanes

Quantitative unique continuation for the semilinear heat equation in a convex domain

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