A local obstruction for elliptic operators with real analytic coefficients on flat germs

Martino Fassina; Yifei Pan

doi:10.5802/afst.1722

Martino Fassina ¹ ; Yifei Pan ²

¹ Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
² Department of Mathematical Sciences, Purdue University Fort Wayne, 2101 East Coliseum Boulevard, Fort Wayne, IN 46805, USA

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 5, pp. 1343-1363.

Résumé
Abstract

Soit $Ω \subset ℝ^{n}, n \geq 2$ , un ensemble ouvert. Pour un opérateur différentiel elliptique $L$ sur $Ω$ avec des coefficients analytiques réels et un point $p \in Ω$ , nous construisons une fonction lisse $g$ avec les propriétés suivantes : $g$ est plat en $p$ et l’équation $L u = g$ n’a pas de solution locale lisse $u$ qui est plate en $p$ .

Let $Ω \subset ℝ^{n}, n \geq 2$ , be an open set. For an elliptic differential operator $L$ on $Ω$ with real analytic coefficients and a point $p \in Ω$ , we construct a smooth function $g$ with the following properties: $g$ is flat at $p$ and the equation $L u = g$ has no smooth local solution $u$ that is flat at $p$ .

Reçu le : 2020-04-03
Accepté le : 2020-11-05
Publié le : 2022-12-08

DOI : 10.5802/afst.1722

Classification : 35J99, 32W99
Mots clés : Elliptic operators, flat functions

Affiliations des auteurs :

Martino Fassina ¹ ; Yifei Pan ²

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {A local obstruction for elliptic operators with real analytic coefficients on flat germs},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1343--1363},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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Martino Fassina; Yifei Pan. A local obstruction for elliptic operators with real analytic coefficients on flat germs. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 5, pp. 1343-1363. doi : 10.5802/afst.1722. https://afst.centre-mersenne.org/articles/10.5802/afst.1722/

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