Polar factorization and pseudo-rearrangements: applications to Pólya–Szegö type inequalities
| Autor: | Roberta Volpicelli, Adele Ferone |
|---|---|
| Přispěvatelé: | A., Ferone, Volpicelli, Roberta, Ferone, Adele, Volpicelli, R. |
| Rok vydání: | 2003 |
| Předmět: |
Polya-Szego type inequalities
Microbiology (medical) Bounded set Measurable function Uniform convergence Immunology Rearrangement Function (mathematics) Type (model theory) Measure (mathematics) Combinatorics Distribution function Factorization Immunology and Allergy Polar factorization Pseudo-rearrangement Mathematics |
| Zdroj: | Nonlinear Analysis: Theory, Methods & Applications. 53:929-949 |
| ISSN: | 0362-546X |
| Popis: | We are interested in the polar factorization of a function f defined in an open bounded set Ω⊆ R N . It is well known that there exists a measure preserving map σ such that f=f ∗ ∘σ where f ∗ is the decreasing rearrangement of f . We prove that, under suitable assumptions, besides the classical polar factorization of f we have f= f u ∘σ where f u is a pseudo-rearrangement of f with respect to the measurable function u and σ is the measure preserving map such that u=u ∗ ∘σ . As an application, we characterize those functions that realize equality in the Polya–Szego inequality. |
| Databáze: | OpenAIRE |
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