{"title":"不适定椭圆方程的最优小波解","authors":"Jinru Wang, Meng Wang","doi":"10.1109/IWCFTA.2012.11","DOIUrl":null,"url":null,"abstract":"In this paper, a Cauchy problem for two-dimensional Lap lace equation in the strip 0 ≤ × ≤ 1 is considered. This is a classical severely ill-posed problem. Connecting Shannon wavelet bases with a spectral integral of the Hermitian operator, we can obtain a regularized solution. Moreover, some sharp stable estimates between the exact solution and it's approximation is also provided.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"386 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal Wavelet Solutions for Ill-posed Elliptic Equations\",\"authors\":\"Jinru Wang, Meng Wang\",\"doi\":\"10.1109/IWCFTA.2012.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a Cauchy problem for two-dimensional Lap lace equation in the strip 0 ≤ × ≤ 1 is considered. This is a classical severely ill-posed problem. Connecting Shannon wavelet bases with a spectral integral of the Hermitian operator, we can obtain a regularized solution. Moreover, some sharp stable estimates between the exact solution and it's approximation is also provided.\",\"PeriodicalId\":354870,\"journal\":{\"name\":\"2012 Fifth International Workshop on Chaos-fractals Theories and Applications\",\"volume\":\"386 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 Fifth International Workshop on Chaos-fractals Theories and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IWCFTA.2012.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IWCFTA.2012.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Optimal Wavelet Solutions for Ill-posed Elliptic Equations
In this paper, a Cauchy problem for two-dimensional Lap lace equation in the strip 0 ≤ × ≤ 1 is considered. This is a classical severely ill-posed problem. Connecting Shannon wavelet bases with a spectral integral of the Hermitian operator, we can obtain a regularized solution. Moreover, some sharp stable estimates between the exact solution and it's approximation is also provided.
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