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Construction of p-energy and associated energy measures on the Sierpiński carpet / Sierpiński carpet上のp-エネルギーと対応するエネルギー測度の構成Shimizu, Ryosuke 26 September 2022 (has links)
京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24262号 / 情博第806号 / 新制||情||136(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)教授 木上 淳, 教授 磯 祐介, 准教授 白石 大典 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM
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Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type SpacesChilders, Kristen Snyder 01 January 2011 (has links)
In [2], Beals, Gaveau and Greiner find the fundamental solution to a 2-Laplace-type equation in a class of sub-Riemannian spaces. This fundamental solution is based on the well-known fundamental solution to the p-Laplace equation in Grushin-type spaces [4] and the Heisenberg group [6]. In this thesis, we look to generalize the work in [2] for a p-Laplace-type equation. After discovering that the "natural" generalization fails, we find two generalizations whose solutions are based on the fundamental solution to the p-Laplace equation.
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