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


Authors: Giovanni Di Fratta and Alberto Fiorenza
Journal: Proc. Amer. Math. Soc. 148 (2020), 2143-2148
MSC (2010): Primary 35D30; Secondary 35B65
DOI: https://doi.org/10.1090/proc/14895
Published electronically: February 13, 2020
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Abstract: We prove a local regularity result for distributional solutions of Poisson's equation with $ L^p$ data. We use a very short argument based on Weyl's lemma and the Riesz-Fréchet representation theorem.


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Giovanni Di Fratta
Affiliation: Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstrae 8-10, 1040 Wien, Austria
Email: giovanni.difratta@asc.tuwien.ac.at

Alberto Fiorenza
Affiliation: Dipartimento di Architettura, Universitá di Napoli Federico II, Via Monteoliveto, 3, I-80134 Napoli, Italy; and Istituto per le Applicazioni del Calcolo “Mauro Picone”, sezione di Napoli, Consiglio Nazionale delle Ricerche, via Pietro Castellino, 111,I-80131 Napoli, Italy
Email: fiorenza@unina.it

DOI: https://doi.org/10.1090/proc/14895
Received by editor(s): April 6, 2019
Received by editor(s) in revised form: October 2, 2019
Published electronically: February 13, 2020
Additional Notes: The first author acknowledges support from the Austrian Science Fund (FWF) through the special research program Taming complexity in partial differential systems (Grant SFB F65).
Communicated by: Ariel Barton
Article copyright: © Copyright 2020 American Mathematical Society