Potential the Oretic study on quasi-regular mappings

拟正则映射的 Oretic 研究潜力

• 批准号: 10440049
• 负责人: MIZUTA Yoshihiro
• 金额: $ 2.94万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10440049/
• 关键词: Potential theory; Complex analysis; quasi-conformal mappings; Elliptic partical differential equations; boundary behaviors

The aim of this study is to investigate boundary behaviors of quasi-conformal mappings, and then apply our methods to the Dirichlet problem for non-linear elliptic equations.In order to complete the present study, we called some meetings with investigators and discussed each other. With the help of this Grant-in-aid for Scientific Research, we successfully had the conferences on potential theory in Suuri-kaiseki-kenkyusyo, Kyoto Sangyo-University, Gifu University and Hiroshima University. Especially, in Hiroshima University, we held the workshop on real and complex analysis with famous Korean mathematicians, whose proceedings will be published soon and will be served as the further development of this study.The Head investigator of this study was invited to the international conferences to present and give a talk. We had the great success in collecting new aspects of this study by the discussions with many famous mathematicians in the world.Each coordinate of quasi-regular mappings are called monotone. It is very useful for us to study monotone functions in general settings, We have obtained interesting results on the boundary behaviors for monotone Sobolev functions in the unit ball. Our results will be widely delivered in some papers.

本研究的目的是研究拟共形映射的边界行为，并将我们的方法应用于非线性椭圆型方程的Dirichlet问题，为了完成本研究，我们召集了一些研究人员进行讨论。在科学研究补助金的帮助下，我们成功地在Suri-kaiseki-kenkyusyo，京都Sangyo-University，岐阜大学和广岛大学举办了势能理论会议。特别是在广岛大学，我们与韩国著名数学家共同举办了真实的复分析研讨会，其论文集即将出版，将作为本研究的进一步发展。本研究的首席研究员被邀请到国际会议上发表演讲。通过与国际上许多著名数学家的讨论，我们在这方面的研究中取得了很大的进展。研究一般情况下的单调函数是非常有用的，我们得到了单位球上单调Sobolev函数的边界行为的有趣结果。我们的研究结果将在一些论文中广泛发表。

项目成果

Y.Mizutani,N.Muramoto and K.Yoshida: "Self-Similar radial solutions to a parabolic system modelling chemotaxis via variational method"Hiroshima Math.J.. 29. 145-160 (1999)

Y.Mizutani、N.Muramoto 和 K.Yoshida：“通过变分方法模拟趋化性的抛物线系统的自相似径向解”Hiroshima Math.J.. 29. 145-160 (1999)

Y. Mizuta and T. Shimomura: "Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball."Acad. Sci. Fenn. Ser. A. I. Math.. 26. 45-60 (1999)

Y. Mizuta 和 T. Shimomura：“单位球中 BLD 和单调 BLD 函数的球形装置的边界限制。”Acad。

水田義弘: "実解析入門"倍風館. 275 (1999)

水田义宏：《实分析导论》Baifukan 275 (1999)。

Y.Mizuta: "Multiple exponential integrability for Riesz potentials of functions in Orlicz classes"Advances in Math.Sci.and Applications. 9. 621-631 (1999)

Y.Mizuta：“Orlicz 类中函数的 Riesz 势的多重指数可积性”数学、科学和应用的进展。