Prescribed conditions at infinity for fractional parabolic and elliptic equations with unbounded coefficients

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Abstract

We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed point-wise conditions at infinity (in space), which can be time-dependent. Moreover, we study the asymptotic behavior of such solutions. We also consider solutions of elliptic equations satisfying appropriate conditions at infinity.
Original languageEnglish
Pages (from-to)105-127
Number of pages23
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume24
Issue number1
DOIs
Publication statusPublished - Jan 2018
Externally publishedYes

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Unbounded Coefficients
Elliptic Equations
Parabolic Equation
Fractional
Infinity
Asymptotic Behavior of Solutions
Existence and Uniqueness of Solutions
Class

Cite this

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title = "Prescribed conditions at infinity for fractional parabolic and elliptic equations with unbounded coefficients",
abstract = "We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed point-wise conditions at infinity (in space), which can be time-dependent. Moreover, we study the asymptotic behavior of such solutions. We also consider solutions of elliptic equations satisfying appropriate conditions at infinity.",
author = "F. Punzo and Enrico Valdinoci",
year = "2018",
month = "1",
doi = "10.1051/cocv/2016077",
language = "English",
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pages = "105--127",
journal = "ESAIM - Control, Optimisation and Calculus of Variations",
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AU - Valdinoci, Enrico

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AB - We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed point-wise conditions at infinity (in space), which can be time-dependent. Moreover, we study the asymptotic behavior of such solutions. We also consider solutions of elliptic equations satisfying appropriate conditions at infinity.

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DO - 10.1051/cocv/2016077

M3 - Article

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EP - 127

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

SN - 1262-3377

IS - 1

ER -