Space-like strong unique continuation for some fractional parabolic equations

Vedansh Arya; Agnid Banerjee; Donatella Danielli; Nicola Garofalo

doi:10.1016/j.jfa.2022.109723

Space-like strong unique continuation for some fractional parabolic equations

Vedansh Arya, Agnid Banerjee, Donatella Danielli, Nicola Garofalo

Mathematical and Statistical Sciences, School of (SoMSS)

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

5 Scopus citations

Abstract

In this paper we establish the space-like strong unique continuation for nonlocal equations of the type (∂_t−Δ)^su=Vu, for 0<s<1. The proof of our main result, Theorem 1.1, is achieved via a conditional elliptic type doubling property for solutions to the appropriate extension problem, followed by a blowup analysis.

Original language	English (US)
Article number	109723
Journal	Journal of Functional Analysis
Volume	284
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2022.109723
State	Published - Jan 1 2023

Keywords

Monotonicity of adjusted frequency
Nonlocal parabolic equations
Strong unique continuation

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2022.109723

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abstract = "In this paper we establish the space-like strong unique continuation for nonlocal equations of the type (∂t−Δ)su=Vu, for 0",

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author = "Vedansh Arya and Agnid Banerjee and Donatella Danielli and Nicola Garofalo",

note = "Funding Information: A. Banerjee is supported in part by SERB Matrix grant MTR/2018/000267 and by Department of Atomic Energy, Government of India , under project no. 12-R & D-TFR-5.01-0520 . N. Garofalo is supported in part by a Progetto SID: “Non-local Sobolev and isoperimetric inequalities”, University of Padova , 2019. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

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AU - Arya, Vedansh

AU - Banerjee, Agnid

AU - Danielli, Donatella

AU - Garofalo, Nicola

N1 - Funding Information: A. Banerjee is supported in part by SERB Matrix grant MTR/2018/000267 and by Department of Atomic Energy, Government of India , under project no. 12-R & D-TFR-5.01-0520 . N. Garofalo is supported in part by a Progetto SID: “Non-local Sobolev and isoperimetric inequalities”, University of Padova , 2019. Publisher Copyright: © 2022 Elsevier Inc.

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AB - In this paper we establish the space-like strong unique continuation for nonlocal equations of the type (∂t−Δ)su=Vu, for 0

KW - Monotonicity of adjusted frequency

KW - Nonlocal parabolic equations

KW - Strong unique continuation

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Space-like strong unique continuation for some fractional parabolic equations

Abstract

Keywords

ASJC Scopus subject areas

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