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2015 Fiscal Year Final Research Report

Refinement of classical inequalities and its application to elliptic variational problems

Research Project

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Project/Area Number 24540157
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionIbaraki University

Principal Investigator

Horiuchi Toshio  茨城大学, 理学部, 教授 (80157057)

Co-Investigator(Kenkyū-buntansha) NAKAI EIICHI  茨城大学, 理学部, 教授 (60259900)
SHIMOMURA KATUNORI  茨城大学, 理学部, 教授 (00201559)
ANDO HIROSHI  茨城大学, 理学部, 講師 (60292471)
Co-Investigator(Renkei-kenkyūsha) HOSHIRO TOSHIHIKO  兵庫県立大学, 物質理学研究科, 教授 (40211544)
SATO TOKUSHI  東北大学, 理学研究科, 助教 (00261545)
Project Period (FY) 2012-04-01 – 2016-03-31
KeywordsCKN型不等式 / ハーディ不等式 / ソボレフ不等式 / 楕円型変分問題 / ミッシング・ターム / p-ラプラシアン / 加藤の不等式 / 強最大値原理
Outline of Final Research Achievements

(1) Existence of the solutions for the best constants of the Caffarelli-Kohn-Nirenberg type inequalities, continuity with respect to parameters of the best constant, symmetry breaking were studied systematically. For p=1, the Caffarelli-Kohn-Nirenberg type inequalities were established by effective use of isoperimetric inequalities, and symmetry breaking in p=1 was proved. (2) A theory of super logarithm based on logarithmic infinite product was introduced, and existence of infinitely many missing term was shown for the weighted Hardy type inequalities. (3) Differential equations characterizing super logarithm was studied to deal with elliptic equations with nonlinear term of very fast growth order.

Free Research Field

偏微分方程式論

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Published: 2017-05-10  

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