Abstract
The paper is related to the question of uniqueness in the inverse logarithmic potential problem. This question is to find the conditions on which two domains D 1 and D 2 producing the same external potential must coincide. Assuming the general hypothesis of regularity and an additional condition of connectivity of (D1∪D2)c, we prove a theorem of uniqueness in the case when one of the domains is a lemniscate. The main tool is one lemma for Cauchy's potential due to M. Sakai. We give a simple proof of its extension to Newtonian potential.
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Références
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Loukianov, O.Y. Problème inverse de la théorie du potentiel logarithmique pour les lemniscates. Potential Anal 1, 337–341 (1992). https://doi.org/10.1007/BF00301786
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DOI: https://doi.org/10.1007/BF00301786