Proceedings of the American Mathematical Society, volume 148, issue 5, pages 2143-2148

A short proof of local regularity of distributional solutions of Poisson’s equation

Giovanni Di Fratta ¹

Alberto Fiorenza ²

Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstrae 8-10, 1040 Wien, Austria |

Dipartimento di Architettura, UniversitÃ¡ di Napoli Federico II, Via Monteoliveto, 3, I-80134 Napoli, Italy; and Istituto per le Applicazioni del Calcolo âMauro Piconeâ, sezione di Napoli, Consiglio Nazionale delle Ricerche, via Pietro Castellino, 111,I-80131 Napoli, Italy

Publication type: Journal Article

Publication date: 2019-10-23

American Mathematical Society

Journal: Proceedings of the American Mathematical Society

scimago Q1

SJR: 0.837

CiteScore: 1.7

Impact factor: 0.8

ISSN: 00029939, 10886826

DOI: 10.1090/proc/14895

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General Mathematics

Applied Mathematics

Abstract

We prove a local regularity result for distributional solutions of Poisson’s equation withLpL^pdata. We use a very short argument based on Weyl’s lemma and the Riesz-Fréchet representation theorem.

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Nonlinear Analysis, Theory, Methods and Applications	Nonlinear Analysis, Theory, Methods and Applications, 1, 20% Nonlinear Analysis, Theory, Methods and Applications 1 publication, 20%
Computers and Mathematics with Applications	Computers and Mathematics with Applications, 1, 20% Computers and Mathematics with Applications 1 publication, 20%
Proceedings of the American Mathematical Society	Proceedings of the American Mathematical Society, 1, 20% Proceedings of the American Mathematical Society 1 publication, 20%
Calculus of Variations and Partial Differential Equations	Calculus of Variations and Partial Differential Equations, 1, 20% Calculus of Variations and Partial Differential Equations 1 publication, 20%
Annals of Global Analysis and Geometry	Annals of Global Analysis and Geometry, 1, 20% Annals of Global Analysis and Geometry 1 publication, 20%
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Elsevier	Elsevier, 2, 40% Elsevier 2 publications, 40%
Springer Nature	Springer Nature, 2, 40% Springer Nature 2 publications, 40%
American Mathematical Society	American Mathematical Society, 1, 20% American Mathematical Society 1 publication, 20%
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Publisher

American Mathematical Society

Journal

Proceedings of the American Mathematical Society

scimago Q1

SJR

0.837

CiteScore

1.7

Impact factor

0.8

ISSN

00029939 (Print)

10886826 (Electronic)

A short proof of local regularity of distributional solutions of Poisson’s equation

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