| 张琴,冯小高.加权全能量最小的圆环形变*[J].数学年刊A辑,2022,43(4):387~398 |
| 加权全能量最小的圆环形变* |
| Deformation of Annuli with Smallest Total Weighted Energy |
| Received:September 07, 2021 Revised:September 24, 2022 |
| DOI：10.16205/j.cnki.cama.2022.0025 |
| 中文关键词: 加权全能量, 加权调和能量, 加权偏差, ODE |
| 英文关键词:Total weighted energy, Weighted harmonic energy, Weighted distortion, ODE |
| 基金项目:自然科学基金 (No.11701459)和西华师范大学科研启动项目(No.17E088) |
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| 中文摘要: |
| 主要考虑如下加权全能量极值问题:inf/h ∈?(A1,A2)α?A1(|hN |2 + |hT |2)1/|h(z)|2dz + β?A1|hN |2 + |hT |2/J(z, h)1|z|2dz,其中H(A1, A2), 代表从圆环 A1 到圆环 A2 的所有保向同胚映射的集合.研究得到唯一的极值映射为径向拉伸映射. 这将 [Iwaniec T, Onninen J. Hyperelastic deformations of smallest total energy [J].Arch Rational Mech Anal, 2009, 194:927–986.]的结果推广至非欧情形. 同时, 也分别研究了圆环上的加权调和能量的极值问题与加权偏差的极值问题. |
| 英文摘要: |
| In this paper, the authors mainly study the following extremal problem for total weighted energy inf/h ∈?(A1,A2)α?A1(|hN |2 + |hT |2)1/|h(z)|2dz + β?A1|hN |2 + |hT |2/J(z, h)1|z|2dz,where the class H(A1, A2) consists of orientation preserving homeomorphisms between annuli A1 and A1. They get that the unique extremal mapping is a certain radial mapping. This extends the result of [Iwaniec, T. and Onninen, J., Hyperelastic deformations of smallest total energy, Arch. Rational Mech. Anal., 2009, vol. 194, pp. 927–986] to non-Euclidean version. Meanwhile, they also consider the extremal problems for weighted harmonic energy and weighted distortion on annuli, respectively. |
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