John-Stromberg 不等式與 VMO 函數類;The John-Stromberg Inequality and Vmo Type Spaces

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/84741

Title:	John-Stromberg 不等式與 VMO 函數類;The John-Stromberg Inequality and Vmo Type Spaces
Authors:	林欽誠
Contributors:	數學系
Keywords:	John-Stromberg 不等式;仿射 VMO;Monge-Ampere 方程;正則性;John-Stromberg inequality;affine VMO;Monge-Ampere equation;regularity
Date:	2020-12-08
Issue Date:	2020-12-09 10:49:43 (UTC+8)
Publisher:	科技部
Abstract:	我們研究架構於一般集合族上的 John-Stromberg 不等式，而這個集合族滿足拓樸測度空間上的一些公設條件，包含歐式空間上的嚴格凸函數所衍生的 section 族。也會引進對應的仿射 VMO 空間，並研究該空間的相關性質。有了上述相關結果後，我們就有可能證明局部非退化 Monge-Ampere 方程解的正則理論。 ;We study the John-Stromberg inequality over families of general sets in topological measure spaces satisfying certain axioms, which include families of sections induced by strictly convex functions in $\Bbb R^n$. Affine VMO space is introduced and studied. Then we will present a regularity theory for entire solutions of locally nondegenerate Monge-Ampere equation $\det D^2u=f(x)$ with $f$ in local affine VMO space.
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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