Minimal area problems for functions with integral representation

Dov Aharonov; Harold S. Shapiro; Alexander Yu Solynin

doi:10.1007/BF02790271

Minimal area problems for functions with integral representation

Dov Aharonov, Harold S. Shapiro, Alexander Yu Solynin

Mathematics and Statistics

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3 Scopus citations

Abstract

We study the minimization problem for the Dirichlet integral in some standard classes of analytic functions. In particular, we solve the minimal area a₂ -problem for convex functions and for typically real functions. The latter gives a new solution to the minimal area a₂ -problem for the class 5 of normalized univalent functions in the unit disc.

Original language	English
Pages (from-to)	83-111
Number of pages	29
Journal	Journal d'Analyse Mathematique
Volume	98
DOIs	https://doi.org/10.1007/BF02790271
State	Published - 2006

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title = "Minimal area problems for functions with integral representation",

abstract = "We study the minimization problem for the Dirichlet integral in some standard classes of analytic functions. In particular, we solve the minimal area a2 -problem for convex functions and for typically real functions. The latter gives a new solution to the minimal area a2 -problem for the class 5 of normalized univalent functions in the unit disc.",

author = "Dov Aharonov and Shapiro, {Harold S.} and Solynin, {Alexander Yu}",

note = "Funding Information: *Supported by NSF grant DMS-0412908.",

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journal = "Journal d'Analyse Mathematique",

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AU - Aharonov, Dov

AU - Shapiro, Harold S.

AU - Solynin, Alexander Yu

N1 - Funding Information: *Supported by NSF grant DMS-0412908.

PY - 2006

Y1 - 2006

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AB - We study the minimization problem for the Dirichlet integral in some standard classes of analytic functions. In particular, we solve the minimal area a2 -problem for convex functions and for typically real functions. The latter gives a new solution to the minimal area a2 -problem for the class 5 of normalized univalent functions in the unit disc.

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U2 - 10.1007/BF02790271

DO - 10.1007/BF02790271

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VL - 98

SP - 83

EP - 111

JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

ER -

Minimal area problems for functions with integral representation

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