Rearrangements of functions

Crowe, J.A.; Zweibel, John; Rosenbloom, P. C.

doi:10.1016/0022-1236(86)90067-4

Cited by 77 publications

(49 citation statements)

References 4 publications

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“…A continuous version of the above rearrangement inequality (e.g., see Lorentz 1953 andCrowe, Zweibel, andRosenbloom 1986) shows that PAM is optimal if and only if f is supermodular, and NAM is optimal if and only if f is submodular. Also, the ShapleyShubik linear programming derivation of the optimal assignment, core allocations, and Walrasian equilibrium extends to continuous models Zame 1992, 1999).…”

Section: The Large-market Casementioning

confidence: 99%

Sorting through Search and Matching Models in Economics

Chade

Eeckhout²,

Smith

2017

Journal of Economic Literature

146

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Toward understanding assortative matching, this is a self-contained introduction to research on search and matching. We first explore the nontransferable and perfectly transferable utility matching paradigms, and then a unifying imperfectly transferable utility matching model. Motivated by some unrealistic predictions of frictionless matching, we flesh out the foundational economics of search theory. We then revisit the original matching paradigms with search frictions. We finally allow informational frictions that often arise, such as in college-student sorting. (JEL C78, D82, D83, I23, J12)

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Section: The Large-market Casementioning

confidence: 99%

Sorting through Search and Matching Models in Economics

Chade

Eeckhout²,

Smith

2017

Journal of Economic Literature

146

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“…The ideas of Crowe, Zweibel and Rosenbloom [7], and of Alberti [1] can be generalized to embrace the case of the increasing rearrangement. Proposition 2.14.…”

Section: Definition 26 the Increasing Rearrangement Ofmentioning

confidence: 99%

Universal approximation of symmetrizations by polarizations

Schaftingen

2005

Proc. Amer. Math. Soc.

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“…The following theorem (for a proof see [CZR,Theorem 3, Corollary 1]) will be very useful for approximations of the rearranged functions: Theorem 3.1 (Nonexpansivity of rearrangements). Let T be a rearrangement.…”

Section: Rearrangementsmentioning

confidence: 99%

An approach to symmetrization via polarization

Brock¹,

Solynin²

1999

Trans. Amer. Math. Soc.

164

161

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Abstract. We prove that the Steiner symmetrization of a function can be approximated in L p (R n ) by a sequence of very simple rearrangements which are called polarizations. This result is exploited to develop elementary proofs of many inequalities, including the isoperimetric inequality in Euclidean space. In this way we also obtain new symmetry results for solutions of some variational problems. Furthermore we compare the solutions of two boundary value problems, one of them having a "polarized" geometry and we show some pointwise inequalities between the solutions. This leads to new proofs of well-known functional inequalities which compare the solutions of two elliptic or parabolic problems, one of them having a "Steiner-symmetrized" geometry. The method also allows us to investigate the case of equality in the inequalities. Roughly speaking we prove that the equality sign is valid only if the original problem has the symmetrized geometry.

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Rearrangements of functions

Cited by 77 publications

References 4 publications

Sorting through Search and Matching Models in Economics

Sorting through Search and Matching Models in Economics

Universal approximation of symmetrizations by polarizations

An approach to symmetrization via polarization

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