Balls are maximizers of the Riesz-type functionals with supermodular integrands
نویسندگان
چکیده
منابع مشابه
Balls Are Maximizers of the Riesz-type Functionals with Supermodular Integrands
Over the last decades, one field of intense research activity has been the study of extremals of integral functionals. The Riesz-type kind has attracted growing attention and played a crucial role in the resolution of Choquard’s conjecture in a breakthrough paper by E. H. Lieb [1]. The determination of cases of equality in the Riesz-rearrangement inequality has also received a large amount of i...
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Abstract The inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands of the form F (u1, . . . , um) where F is supermodular; in particular, they hold when F has nonnegative mixed second derivatives ∂i∂jF for all i 6= j. This paper...
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A Kotz-Riesz-Type Distribution
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ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata
سال: 2009
ISSN: 0373-3114,1618-1891
DOI: 10.1007/s10231-009-0114-9