Banach空间L_p（Ω）中非齐次不适定椭圆边值问题的最小范数极值解

Abstract

Abstract:

该文对Ｂａｎａｃｈ空间犔犘（Ω）中二阶椭圆方程非齐次不适定Ｎｅｕｍａｎｎ问题，引入伪变分解的概念，应用Ｂａｎａｃｈ空间几何及［３］中关于Ｂａｎａｃｈ空间中线性算子的ＭｏｏｒｅＰｅｎｒｏｓｅ广义逆，证明了上述伪变分解为最小范数极值解，从而为适定的．

Key words: Ｎｅｕｍａｎｎ边值问题, 伪变分解, ＭｏｏｒｅＰｅｎｒｏｓｅ广义逆, 最小范数极值解

CLC Number:

46B20

WANG Yu-Wen, YU Jin-Feng. The Minimal Norm Extrimal Solution to the Non-Homogeneous III-Posed Boundary Value Problem in Banach Space L^p(Ω)[J].Acta mathematica scientia,Series A, 2001, 21(2): 191-200.

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References

１ＡｄａｍｓＲＡ．Ｓｏｂｏｌｅｖｓｐａｃｅ．Ｂｅｒｌｉｎ，Ｈｅｉｄｅｌｂｅｒｇ，ＮｅｗＹｏｒｋ：ＡｃａｄｅｍｉｃＰｒｅｓｓ，１９７８
２　ＴｒｅｖｅｓＦ．Ｂａｓｉｃｌｉｎｅａｒｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．Ｉｎｃ：ＡｃａｄｅｍｉｃＰｒｅｓｓ，Ｉｎｃ，１９７５
３　ＬｉｏｎｓＪＬ，ＭａｇｅｎｓＥ．ＮｏｎＨｏｍｏｇｅｎｅｏｕｓｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓａｎｄａｐｐｌｉｃａｔｉｏｎｓＩ———ＩＩＩ．ＮｅｗＹｏｒｋＨｅｉｄｅｌｂｅｒｇＢｅｒｌｉｎ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９７３
４　王玉文，李志伟．Ｂａｎａｃｈ空间中ＭｏｏｒｅＰｅｎｒｏｓｅ广义逆与不适定边值问题．系统科学与数学，１９９５，１５（２）：１７５～１８５
５　ＷａｎｇＹＷ．ＴｈｅｇｅｎｅｒａｌｉｚｅｄｉｎｖｅｒｓｅｏｐｅｒａｔｏｒｓｉｎＢａｎａｃｈｓｐａｃｅｓ．ＢｕｌｌｅｔｉｎｏｆｔｈｅＰｏｌｉｓｈＡｃａｄＳｃｉＭａｔｈ，１９８９，７～１２：４３３～４４１
６　ＰｌｕｃｉｅｎｎｉｋＲ，Ｗａｎｇ，ＹＷ．ＭｅｔｒｉｃｐｒｏｊｅｃｔｉｏｎａｎｄｂｅｓｔａｐｐｒｏｘｉｍａｔｉｏｎｓｉｎＢｏｃｈｎｅｒＯｒｉｌｉｃｚｓｐａｃｅ．ＲｅｖｉｓｔａＭａｔｈＵｎｉｖＣｏｍｐＭａｄｒｉｄ，１９９４，７（１）
７　马吉溥．关于犚（犃犡）闭的连续算子族犃犡的Ｍｏｏｒｅｐｅｎｒｏｓｅ广义逆连续的充要条件．中国科学（Ａ），１９９０，（６）：５６１～５６８
８　史树中．凸分析．上海：上海科技出版社，１９９０
９　ＬｏｃｋｅｒＪ．Ｆｕｎｃｔｉｏｎａｌａｎａｌｙｓｉｓａｎｄｔｗｏｐｏｉｎｔｄｉｆｆｅｒｅｎｔｉａｌｏｐｅｒａｔｏｒｓ．ＮｅｗＹｏｒｋ：ＬｏｎｇｍａｎＳｃｉｅｎｔｉｆｉｃＴｅｃｈｎｉｃａｌ，１９８６
１０　王玉文，于金凤．Ｂａｎａｃｈ空间中一类度量投影的判据及表达式．数学物理学报，２０００，２０（４）

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The Minimal Norm Extrimal Solution to the Non-Homogeneous III-Posed Boundary Value Problem in Banach Space L^p(Ω)

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