Lp theory for fractional gradient PDE with VMO coefficients

Armin Schikorra; Tien Tsan Shieh; Daniel Eli Spector

doi:10.4171/RLM/714

L^p theory for fractional gradient PDE with VMO coefficients

Armin Schikorra, Tien Tsan Shieh, Daniel Eli Spector

Department of Applied Mathematics

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

16 Scopus citations

Abstract

In this paper, we prove L p estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are VMO. In particular, our work extends the optimal regularity known in the second order elliptic setting to a spectrum of fractional order elliptic equations.

Original language	English
Pages (from-to)	433-443
Number of pages	11
Journal	Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume	26
Issue number	4
DOIs	https://doi.org/10.4171/RLM/714
State	Published - 2015

Keywords

Commutators
Fractional elliptic PDE
VMO coefficients

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10.4171/RLM/714

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title = "Lp theory for fractional gradient PDE with VMO coefficients",

abstract = "In this paper, we prove L p estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are VMO. In particular, our work extends the optimal regularity known in the second order elliptic setting to a spectrum of fractional order elliptic equations.",

keywords = "Commutators, Fractional elliptic PDE, VMO coefficients",

author = "Armin Schikorra and Shieh, {Tien Tsan} and Spector, {Daniel Eli}",

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AU - Schikorra, Armin

AU - Shieh, Tien Tsan

AU - Spector, Daniel Eli

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AB - In this paper, we prove L p estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are VMO. In particular, our work extends the optimal regularity known in the second order elliptic setting to a spectrum of fractional order elliptic equations.

KW - Commutators

KW - Fractional elliptic PDE

KW - VMO coefficients

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U2 - 10.4171/RLM/714

DO - 10.4171/RLM/714

M3 - Article

AN - SCOPUS:84944190689

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VL - 26

SP - 433

EP - 443

JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

IS - 4

ER -

L^p theory for fractional gradient PDE with VMO coefficients

Abstract

Keywords

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