On a reverse Kohler-Jobin inequality

Luca Briani ^[1] ; Giuseppe Buttazzo ^[2] ; Serena Guarino Lo Bianco ^[3]
1. [1] Technical University Munich
  
  Technical University Munich
  
  Kreisfreie Stadt München, Alemania
2. [2] University of Pisa
  
  University of Pisa
  
  Pisa, Italia
3. [3] University of Modena and Reggio Emilia
  
  University of Modena and Reggio Emilia
  
  Módena, Italia
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Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 3, 2024, págs. 913-930
Idioma: inglés
DOI: 10.4171/RMI/1455
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- In this paper, we consider the shape optimization problems for the quantities λ(Ω)Tq(Ω), where Ω varies among open sets of Rd with a prescribed Lebesgue measure. While the characterization of the infimum is completely clear, the same does not happen for the maximization in the case q>1. We prove that for q large enough a maximizing domain exists among quasi-open sets and that the ball is optimal among nearly spherical domains.In this paper, we consider the shape optimization problems for the quantities λ(Ω)Tq(Ω), where Ω varies among open sets of Rd with a prescribed Lebesgue measure. While the characterization of the infimum is completely clear, the same does not happen for the maximization in the case q>1. We prove that for q large enough a maximizing domain exists among quasi-open sets and that the ball is optimal among nearly spherical domains.