具有强竞争的竞争扩散平流系统的均匀Lipschitz界

IF 1 4区数学

Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-05-18 DOI:10.4236/AM.2021.125027

Tingwei Huang, Shan Zhang

{"title":"具有强竞争的竞争扩散平流系统的均匀Lipschitz界","authors":"Tingwei Huang, Shan Zhang","doi":"10.4236/AM.2021.125027","DOIUrl":null,"url":null,"abstract":"We prove the uniform Lipschitz bound of solutions for a nonlinear elliptic system modeling the steady state of populations that compete in a heterogeneous environment. This extends known quasi-optimal regularity results and covers the optimal case for this problem. The proof relies upon the blow-up technique and the almost monotonicity formula by Caffarelli, Jerison and Kenig.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2021-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Uniform Lipschitz Bound for a Competition Diffusion Advection System with Strong Competition\",\"authors\":\"Tingwei Huang, Shan Zhang\",\"doi\":\"10.4236/AM.2021.125027\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the uniform Lipschitz bound of solutions for a nonlinear elliptic system modeling the steady state of populations that compete in a heterogeneous environment. This extends known quasi-optimal regularity results and covers the optimal case for this problem. The proof relies upon the blow-up technique and the almost monotonicity formula by Caffarelli, Jerison and Kenig.\",\"PeriodicalId\":55568,\"journal\":{\"name\":\"Applied Mathematics-A Journal of Chinese Universities Series B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2021-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics-A Journal of Chinese Universities Series B\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4236/AM.2021.125027\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4236/AM.2021.125027","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

我们证明了一类非线性椭圆系统解的一致Lipschitz界，该系统模拟了异质环境中竞争种群的稳态。这扩展了已知的准最优正则性结果，并涵盖了该问题的最优情况。这个证明依靠的是放大法和卡法雷利、杰里逊和凯尼格的几乎单调公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Uniform Lipschitz Bound for a Competition Diffusion Advection System with Strong Competition

We prove the uniform Lipschitz bound of solutions for a nonlinear elliptic system modeling the steady state of populations that compete in a heterogeneous environment. This extends known quasi-optimal regularity results and covers the optimal case for this problem. The proof relies upon the blow-up technique and the almost monotonicity formula by Caffarelli, Jerison and Kenig.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied Mathematics-A Journal of Chinese Universities Series B MATHEMATICS, APPLIED-

自引率

10.00%

发文量

期刊介绍： Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects. The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry. Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.