On a new class of fractional partial differential equations

Tien Tsan Shieh; Daniel E. Spector

doi:10.1515/acv-2014-0009

On a new class of fractional partial differential equations

Tien Tsan Shieh
, Daniel E. Spector

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

89 Citations (Scopus)

Abstract

In this paper, we study a new class of fractional partial differential equations which are obtained by minimizing variational problems in fractional Sobolev spaces. We introduce a notion of fractional gradient which has the potential to extend many classical results in the Sobolev spaces to the nonlocal and fractional setting in a natural way.

Original language	English
Pages (from-to)	321-336
Number of pages	16
Journal	Advances in Calculus of Variations
Volume	8
Issue number	4
DOIs	https://doi.org/10.1515/acv-2014-0009
Publication status	Published - 2015 Oct 1
Externally published	Yes

Keywords

Bessel potential spaces
Fractional gradient
fractional Sobolev inequalities
fractional partial differential equations

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1515/acv-2014-0009

Cite this

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title = "On a new class of fractional partial differential equations",

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keywords = "Bessel potential spaces, Fractional gradient, fractional Sobolev inequalities, fractional partial differential equations",

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AU - Spector, Daniel E.

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KW - Fractional gradient

KW - fractional Sobolev inequalities

KW - fractional partial differential equations

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On a new class of fractional partial differential equations

Abstract

Keywords

ASJC Scopus subject areas

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