{"title":"R2中的梯度变分问题","authors":"R. Kenyon, I. Prause","doi":"10.1215/00127094-2022-0036","DOIUrl":null,"url":null,"abstract":"We prove a new integrability principle for gradient variational problems in $\\mathbb{R}^2$, showing that solutions are explicitly parameterized by $\\kappa$-harmonic functions, that is, functions which are harmonic for the laplacian with varying conductivity $\\kappa$, where $\\kappa$ is the square root of the Hessian determinant of the surface tension.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Gradient variational problems in R2\",\"authors\":\"R. Kenyon, I. Prause\",\"doi\":\"10.1215/00127094-2022-0036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a new integrability principle for gradient variational problems in $\\\\mathbb{R}^2$, showing that solutions are explicitly parameterized by $\\\\kappa$-harmonic functions, that is, functions which are harmonic for the laplacian with varying conductivity $\\\\kappa$, where $\\\\kappa$ is the square root of the Hessian determinant of the surface tension.\",\"PeriodicalId\":11447,\"journal\":{\"name\":\"Duke Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Duke Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1215/00127094-2022-0036\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Duke Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00127094-2022-0036","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove a new integrability principle for gradient variational problems in $\mathbb{R}^2$, showing that solutions are explicitly parameterized by $\kappa$-harmonic functions, that is, functions which are harmonic for the laplacian with varying conductivity $\kappa$, where $\kappa$ is the square root of the Hessian determinant of the surface tension.
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