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arXiv · 2004.11955

Quelques propri\'et\'es qualitatives pour le probl\`eme de surfaces de quadrature dans le plan

Mohammed Barkatou
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Abstract

In this paper, we begin by giving a necessary and sufficient condition of existence for the quadrature surfaces problem in the case where the term source is a uniform density supported by a segment. Then, we use the Steiner continuous symmetrization to prove that the obtained solution is symmetric with respect the x-coordinate axis and that its boundary is analytic. ----------- Dans ce papier, nous commen\c{c}ons par donner une condition n\'ecessaire et suffisante d'existence de solutions pour le probl\`eme de surfaces de quadrature dans le cas o\`u le terme source est une densit\'e support\'ee par un segment. Ensuite, en utilisant la sym\'etrisation de Steiner continue, nous montrons que la solution obtenue est sym\'etrique par rapport \`a l'axe des abscisses et que son bord est analytique.

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Mohammed Barkatou. 2020-04-24. Quelques propri\'et\'es qualitatives pour le probl\`eme de surfaces de quadrature dans le plan. https://arxiv.org/abs/2004.11955

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