| 冯小高.两矩形上的全偏差[J].数学年刊A辑,2020,41(2):163~174 |
| 两矩形上的全偏差 |
| Total Distortion of Mapping Between Rectangles |
| Received:July 14, 2018 |
| DOI：10.16205/j.cnki.cama.2020.0012 |
| 中文关键词: 全偏差, 调和能量, 偏差函数 |
| 英文关键词:otal distortion, Harmonic energy, Distortion function |
| 基金项目:国家自然科学基金 (No.\,11701459), 四川省教育厅一般科研项目(No.\,17ZB0431)和西华师范大学科研启动项目(No.\,17E088) |
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| 中文摘要: |
| 考虑如下极值问题的存在性和唯一性:inf_{h\in\mathfrak{H\mathfrak{}}}\Big\{\alpha\iint_{Q_{2}}\mathbb{K}(w,h^{-1})\rmd u\rmd v+\beta\iint_{Q_{1}}\mathbb{K}(z,h)\rmd x\rmd y\Big\},其中mathfrak{H}代表从矩形Q1到矩形Q2并保持端点且具有有限偏差的所有同胚映射的集合. |
| 英文摘要: |
| This paper considers the existence and uniqueness of minimiser of the following problem inf_{h\in\mathfrak{H\mathfrak{}}}\Big\{\alpha\iint_{Q_{2}}\mathbb{K}(w,h^{-1})\rmd u\rmd v +\beta\iint_{Q_{1}}\mathbb{K}(z,h)\rmd x\rmd y\Big\} under some conditions, where mathfrak{H}denotes the set of all homeomorphisms with finite distortion between two rectangles Q_{1}and Q_{2}taking vertices into vertices. |
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