• Corpus ID: 117101589

Bellman partial differential equation and the hill property for classical isoperimetric problems

@article{Ivanisvili2015BellmanPD,
  title={Bellman partial differential equation and the hill property for classical isoperimetric problems},
  author={Paata Ivanisvili and Alexander Volberg},
  journal={arXiv: Analysis of PDEs},
  year={2015}
}
The goal of this note is to have a systematic approach to generating isoperimetric inequalities from two concrete type of PDEs. We call these PDEs Bellman type because a totally analogous equations happen to rule many sharp estimates for singular integrals in harmonic analysis, and such estimates were obtained with the use of Hamilton--Jacobi--Bellman PDE. We show how classical inequalities of Brascamp--Lieb, Prekopa--Leindler, Ehrhard are particular case of this scheme, which allows us to… 
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