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On an isoperimetric inequality and various methods for the Bernoulli’s free boundary problems

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Abstract

This survey paper on the Bernoulli’s free boundary problems, deals with some important questions of geometric analysis of optimal shapes. Isoperimetric inequality is discussed and other geometric qualitative properties such as symmetry and convexity properties. A comparison of diffrent approaches to establish existence solution of the Bernoulli’s free boundary problems is done followed by some questions on spectral geometry, the numerical analysis and the analysis on manifolds of the problems studied.

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  1. Laboratoire de Mathématique de la Décision et d’Analyse Numérique, FASEG, Université Cheikh Anta Diop de Dakar, BP 16 889, Dakar-Fann, Senegal

    Diaraf Seck

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  1. Diaraf Seck
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Seck, D. On an isoperimetric inequality and various methods for the Bernoulli’s free boundary problems. São Paulo J. Math. Sci. 10, 36–59 (2016). https://doi.org/10.1007/s40863-015-0012-6

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