Sobolev Mappings and Energy-Integrals in Mathematical Models of Nonlinear Elasticity

非线性弹性数学模型中的索博列夫映射和能量积分

基本信息

  • 批准号:
    1301558
  • 负责人:
  • 金额:
    $ 38万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2013
  • 资助国家:
    美国
  • 起止时间:
    2013-06-01 至 2018-05-31
  • 项目状态:
    已结题

项目摘要

The proposal continues a long term research program of the PI to advance variational techniques in Geometric Function Theory with applied disciplines in mind. It provides an in-depth analysis of the concept of energy-minimal deformations between Euclidean domains (predominantly, traction free problems in dimension two). The ambition is to gain insights into the many new phenomena encountered in the Calculus of Variations, Minimal Surfaces, Nonlinear Elasticity, Material Science, and so forth. Historical example would be the celebrated mathematical structure -Teichmüller spaces, where one seeks to minimize the supremum norm of the distortion function. Other examples could be cited. We shall minimize the integral mean distortion instead. The existence and uniqueness of the mappings slipping along the boundary (traction free) with smallest mean distortion takes the challenge to a whole new level. The project continues the efforts of the PI to bring graduate students and postdoctoral scholars to Geometric Analysis with a wide range of applications, and to help them to mature meaningful interaction with physicists and engineers already in their post-doc phase. This is also a key to motivate young gifted students at school or college to enter mathematics. The program provides such an environment through educational materials (book in progress), Summer/Winter mini-courses, junior-senior seminars. PI has a history of an engaging research climate and strong international interaction on these efforts. He anticipates that the presence of applied fields in the proposal will improve the job opportunities for the PhD students and his numerous co-advisees.
这项建议继续了PI的长期研究计划,以推进几何函数论中的变分技术,并着眼于应用学科。它深入分析了欧几里德区域之间的能量最小变形的概念(主要是二维的无牵引力问题)。其目标是深入了解在变分、极小曲面、非线性弹性、材料科学等课程中遇到的许多新现象。历史上的例子将是著名的数学结构-Teichmüler空间,其中一个人寻求最小化扭曲函数的最高范数。还可以举出其他例子。相反,我们将使积分平均失真最小化。具有最小平均偏差的沿边界(无牵引力)滑动的映射的存在唯一性将挑战带到了一个全新的水平。该项目继续努力使研究生和博士后学者学习具有广泛应用的几何分析,并帮助他们与已经处于博士后阶段的物理学家和工程师进行有意义的互动。这也是激励在校或大学的年轻天才学生进入数学的关键。该计划通过教材(正在出版的书籍)、暑期/冬季迷你课程、初级和高级研讨会提供这样的环境。在这些努力上,PI有着引人入胜的研究氛围和强大的国际互动的历史。他预计,提案中应用领域的存在将改善博士生和他的众多合作顾问的就业机会。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

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Tadeusz Iwaniec其他文献

${\cal H}^1$ -estimates of Jacobians by subdeterminants
  • DOI:
    10.1007/s00208-002-0341-5
  • 发表时间:
    2002-10-01
  • 期刊:
  • 影响因子:
    1.400
  • 作者:
    Tadeusz Iwaniec;Jani Onninen
  • 通讯作者:
    Jani Onninen
Div-curl fields of finite distortion
  • DOI:
    10.1016/s0764-4442(98)80160-2
  • 发表时间:
    1998-10-01
  • 期刊:
  • 影响因子:
  • 作者:
    Tadeusz Iwaniec;Carlo Sbordone
  • 通讯作者:
    Carlo Sbordone
Dynamics of Quasiconformal Fields
On Minimisers of $$L^p$$ -mean Distortion

Tadeusz Iwaniec的其他文献

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{{ truncateString('Tadeusz Iwaniec', 18)}}的其他基金

Variational approach to Geometric Function Theorem, Nonlinear PDEs and Hyperelasticy
几何函数定理、非线性偏微分方程和超弹性的变分法
  • 批准号:
    1802107
  • 财政年份:
    2018
  • 资助金额:
    $ 38万
  • 项目类别:
    Continuing Grant
Conference: Harmonic Analysis, Complex Analysis, Spectral Theory and All That
会议:调和分析、复分析、谱理论等等
  • 批准号:
    1600705
  • 财政年份:
    2016
  • 资助金额:
    $ 38万
  • 项目类别:
    Standard Grant
Extremal Problems in Quasiconformal Geometry and Nonlinear PDEs, an Invitation to n- Harmonic Hyperelasticity
拟共形几何和非线性偏微分方程中的极值问题,n 调和超弹性的邀请
  • 批准号:
    0800416
  • 财政年份:
    2008
  • 资助金额:
    $ 38万
  • 项目类别:
    Continuing Grant
Geometric Analysis of Deformations of Finite Distortiion via Nonlinear PDEs and Null Lagrangians
通过非线性偏微分方程和零拉格朗日量对有限畸变变形进行几何分析
  • 批准号:
    0301582
  • 财政年份:
    2003
  • 资助金额:
    $ 38万
  • 项目类别:
    Continuing Grant
Collaborative Research: FRG: Geometric Function Theory: From Complex Functions to Quasiconformal Geometry and Nonlinear Analysis
合作研究:FRG:几何函数理论:从复杂函数到拟共形几何和非线性分析
  • 批准号:
    0244297
  • 财政年份:
    2003
  • 资助金额:
    $ 38万
  • 项目类别:
    Standard Grant
Foundation of the Geometric Function Theory in R^n: The Governing differential Forms, Variational Integrals and Nonlinear Elasticity
R^n 中的几何函数理论基础:控制微分形式、变分积分和非线性弹性
  • 批准号:
    0070807
  • 财政年份:
    2000
  • 资助金额:
    $ 38万
  • 项目类别:
    Continuing Grant
Quasiconformal Mappings, Harmonic Analysis and Nonlinear Elasticity from the Prospective of PDEs
偏微分方程视角下的拟共形映射、调和分析和非线性弹性
  • 批准号:
    9706611
  • 财政年份:
    1997
  • 资助金额:
    $ 38万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Quasiconformal Analysis and Harmonic Integrals with Applications to Nonlinear Elasticity
数学科学:拟共形分析和调和积分及其在非线性弹性中的应用
  • 批准号:
    9401104
  • 财政年份:
    1994
  • 资助金额:
    $ 38万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Regularity Problems in Nonlinear Potential Theory and Quasiregular Mappings
数学科学:非线性势论和拟正则映射中的正则问题
  • 批准号:
    9208296
  • 财政年份:
    1992
  • 资助金额:
    $ 38万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Regularity Problems for Variational Integrals and Quasiregular Mappings
数学科学:变分积分和拟正则映射的正则问题
  • 批准号:
    9007946
  • 财政年份:
    1990
  • 资助金额:
    $ 38万
  • 项目类别:
    Standard Grant

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Analysis and Geometry of Conformal and Quasiconformal Mappings
共形和拟共形映射的分析和几何
  • 批准号:
    2350530
  • 财政年份:
    2024
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    Standard Grant
Unique Continuation and Regularity of Mappings and Functions in Several Complex Variables
多复变量映射和函数的唯一连续性和正则性
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    2023
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