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KAKEN_16K17623seika.pdf
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変分解析を中心とした非線形楕円型方程式の解構造の研究
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ヘンブン カイセキ オ チュウシン ト シタ ヒセンケイ ダエンガタ ホウテイシキ ノ カイコウゾウ ノ ケンキュウ
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Henbun kaiseki o chūshin to shita hisenkei daengata hōteishiki no kaikōzō no kenkyū
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Nonlinear elliptic partial differential equations having variation structure
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生駒, 典久
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イコマ, ノリヒサ
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Ikoma, Norihisa
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慶應義塾大学・理工学部 (矢上)・准教授
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Research team head
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科研費研究者番号 : 50728342
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2019
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科学研究費補助金研究成果報告書
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2018
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本課題では偏微分方程式の１種である非線形楕円型方程式 (連立系) に対し，その方程式に解が存在するのか，また存在したとすればどのような性質を持つのかについて研究を行った．特に変分構造を持つ方程式 (楕円型作用素の分数冪作用素を含む方程式など) を中心に調べ，ある特定の性質を持った解の構成や解が多重に存在することなどを示すことに成功した．また非線形楕円型方程式と深い関係を持つ関数不等式についても研究を行い，不等式を等式として満たす関数が存在するか，という問に対する解答を与えた．
In this project, the existence of solutions and their properties were studied for nonlinear elliptic partial differential equations. In particular, we treated equations which have variational structure (for instance, equations with fractional operators of elliptic operators). We proved the existence of solutions satisfying some properties and showed the existence of multiple solutions. We also studied a variant of the Trudinger-Moser inequality and found conditions when the inequality is satisfied as an equality. This inequality is related to a certain nonlinear elliptic partial differential equation.
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研究種目 : 若手研究(B)
研究期間 : 2016～2018
課題番号 : 16K17623
研究分野 : 偏微分方程式
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