{"title":"论对称域上分数拉普拉奇的罗宾函数的非退化性","authors":"Alejandro Ortega","doi":"10.1007/s41980-023-00841-0","DOIUrl":null,"url":null,"abstract":"<p>In this work we prove, under symmetry and convexity assumptions on the domain <span>\\(\\Omega \\)</span>, the non- degeneracy at zero of the Hessian matrix of the Robin function for the spectral fractional Laplacian. This work extends to the fractional setting the results of M. Grossi concerning the classical Laplace operator.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"2 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Non-degeneracy of the Robin Function for the Fractional Laplacian on Symmetric Domains\",\"authors\":\"Alejandro Ortega\",\"doi\":\"10.1007/s41980-023-00841-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this work we prove, under symmetry and convexity assumptions on the domain <span>\\\\(\\\\Omega \\\\)</span>, the non- degeneracy at zero of the Hessian matrix of the Robin function for the spectral fractional Laplacian. This work extends to the fractional setting the results of M. Grossi concerning the classical Laplace operator.</p>\",\"PeriodicalId\":9395,\"journal\":{\"name\":\"Bulletin of The Iranian Mathematical Society\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Iranian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s41980-023-00841-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-023-00841-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Non-degeneracy of the Robin Function for the Fractional Laplacian on Symmetric Domains
In this work we prove, under symmetry and convexity assumptions on the domain \(\Omega \), the non- degeneracy at zero of the Hessian matrix of the Robin function for the spectral fractional Laplacian. This work extends to the fractional setting the results of M. Grossi concerning the classical Laplace operator.
期刊介绍：
The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
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