On a Poisson's equation arising from magnetism

Luca Lussardi

doi:10.3934/dcdss.2015.8.769

On a Poisson's equation arising from magnetism

Luca Lussardi

Risultato della ricerca: Contributo in rivista › Articolo in rivista › peer review

1 Citazioni (Scopus)

Abstract

We review the proof of existence and uniqueness of the Poisson's equation $\Delta u=div m=0$ whenever $m$ is a unit $L^2$ vector field on $R^3$ with compact support. By standard linear potential theory we deduce also $H^1$ regularity of the unique weak solution.

Lingua originale	English
pagine (da-a)	769-772
Numero di pagine	4
Rivista	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S
Volume	8
DOI	https://doi.org/10.3934/dcdss.2015.8.769
Stato di pubblicazione	Pubblicato - 2015
Pubblicato esternamente	Sì

Keywords

Poisson equation
Riesz potential

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10.3934/dcdss.2015.8.769

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abstract = "We review the proof of existence and uniqueness of the Poisson's equation $\Delta u=div m=0$ whenever $m$ is a unit $L^2$ vector field on $R^3$ with compact support. By standard linear potential theory we deduce also $H^1$ regularity of the unique weak solution.",

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AB - We review the proof of existence and uniqueness of the Poisson's equation $\Delta u=div m=0$ whenever $m$ is a unit $L^2$ vector field on $R^3$ with compact support. By standard linear potential theory we deduce also $H^1$ regularity of the unique weak solution.

KW - Poisson equation

KW - Riesz potential

KW - Poisson equation

KW - Riesz potential

UR - http://hdl.handle.net/10807/64694

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DO - 10.3934/dcdss.2015.8.769

M3 - Article

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JO - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S

JF - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S

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On a Poisson's equation arising from magnetism

Abstract

Keywords

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