{"title":"Eikonal方程解的光滑性及其水平面的正则点","authors":"I. G. Tsar’kov","doi":"10.1134/S1061920823020127","DOIUrl":null,"url":null,"abstract":"<p> Properties of local solarity and regularity in essentially asymmetric locally uniformly rotund spaces are studied. The results obtained are applied to the study of smooth solutions of the eikonal equation <span>\\(\\|\\nabla u|\\equiv 1\\)</span>. For this purpose, sets of regular points are investigated. Examples of the influence of caustics on the evolution of elliptical galaxies into spiral ones are given. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"259 - 269"},"PeriodicalIF":1.7000,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Smoothness of Solutions of the Eikonal Equation and Regular Points of Their Level Surfaces\",\"authors\":\"I. G. Tsar’kov\",\"doi\":\"10.1134/S1061920823020127\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> Properties of local solarity and regularity in essentially asymmetric locally uniformly rotund spaces are studied. The results obtained are applied to the study of smooth solutions of the eikonal equation <span>\\\\(\\\\|\\\\nabla u|\\\\equiv 1\\\\)</span>. For this purpose, sets of regular points are investigated. Examples of the influence of caustics on the evolution of elliptical galaxies into spiral ones are given. </p>\",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"30 2\",\"pages\":\"259 - 269\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-06-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1061920823020127\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823020127","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Smoothness of Solutions of the Eikonal Equation and Regular Points of Their Level Surfaces
Properties of local solarity and regularity in essentially asymmetric locally uniformly rotund spaces are studied. The results obtained are applied to the study of smooth solutions of the eikonal equation \(\|\nabla u|\equiv 1\). For this purpose, sets of regular points are investigated. Examples of the influence of caustics on the evolution of elliptical galaxies into spiral ones are given.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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