On random weighted Sobolev inequalities on ℝ^{𝕕} and applications | Zendy

Didier Robert | Zendy; Laurent Thomann | Zendy

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On random weighted Sobolev inequalities on ℝ^{𝕕} and applications

Author(s) -

Didier Robert,

Laurent Thomann

Publication year - 2015

Publication title -

contemporary mathematics - american mathematical society

Language(s) - English

Resource type - Reports

SCImago Journal Rank - 0.106

H-Index - 12

eISSN - 1098-3627

pISSN - 0271-4132

DOI - 10.1090/conm/640/12843

Subject(s) - mathematics , sobolev space , sobolev inequality , inequality , pure mathematics , mathematical analysis

International audienceOur aim in this paper is to give an overview of recent results concerning randomization methods applied to Schrödinger equations obtained in [33, 32, 35]. We focus here on properties of the harmonic oscillator and Her-mite functions for simplicity. The general idea is that several well known deterministic results like Sobolev type inequalities are improved in a large extent by introducing some random-ness. This is very useful in particular for N.L.S with supercritical initial data

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