Nonlocal fractional elliptic equations and applications

Veli Shakhmurov; Muhammet Kurulay

doi:10.1002/num.22910

Nonlocal fractional elliptic equations and applications

Veli Shakhmurov, Muhammet Kurulay^*

^*Corresponding author for this work

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

Abstract

The L_p-coercive properties of a nonlocal fractional elliptic equation is studied. Particularly, it is proved that the fractional elliptic operator generated by this equation is sectorial in L_p space and also is a generator of an analytic semigroup. Moreover, by using the L_p-separability properties of the given elliptic operator the maximal regularity of the corresponding nonlocal fractional parabolic equation is established.

Original language	English
Pages (from-to)	923-931
Number of pages	9
Journal	Numerical Methods for Partial Differential Equations
Volume	39
Issue number	2
DOIs	https://doi.org/10.1002/num.22910
Publication status	Published - Mar 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022 Wiley Periodicals LLC.

Keywords

elliptic equations
fractional-differential equations
L-multipliers
maximal L regularity
parabolic equations
Sobolev spaces

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10.1002/num.22910

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abstract = "The Lp-coercive properties of a nonlocal fractional elliptic equation is studied. Particularly, it is proved that the fractional elliptic operator generated by this equation is sectorial in Lp space and also is a generator of an analytic semigroup. Moreover, by using the Lp-separability properties of the given elliptic operator the maximal regularity of the corresponding nonlocal fractional parabolic equation is established.",

keywords = "elliptic equations, fractional-differential equations, L-multipliers, maximal L regularity, parabolic equations, Sobolev spaces",

author = "Veli Shakhmurov and Muhammet Kurulay",

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year = "2023",

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AU - Shakhmurov, Veli

AU - Kurulay, Muhammet

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N2 - The Lp-coercive properties of a nonlocal fractional elliptic equation is studied. Particularly, it is proved that the fractional elliptic operator generated by this equation is sectorial in Lp space and also is a generator of an analytic semigroup. Moreover, by using the Lp-separability properties of the given elliptic operator the maximal regularity of the corresponding nonlocal fractional parabolic equation is established.

AB - The Lp-coercive properties of a nonlocal fractional elliptic equation is studied. Particularly, it is proved that the fractional elliptic operator generated by this equation is sectorial in Lp space and also is a generator of an analytic semigroup. Moreover, by using the Lp-separability properties of the given elliptic operator the maximal regularity of the corresponding nonlocal fractional parabolic equation is established.

KW - elliptic equations

KW - fractional-differential equations

KW - L-multipliers

KW - maximal L regularity

KW - parabolic equations

KW - Sobolev spaces

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DO - 10.1002/num.22910

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EP - 931

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 2

ER -

Nonlocal fractional elliptic equations and applications

Abstract

Bibliographical note

Keywords

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