一類n—能量泛函極小元的收斂性質(zhì).pdf

1、南京師范大學(xué)碩士學(xué)位論文一類n能量泛函極小元的收斂性質(zhì)姓名：張新勝申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：數(shù)學(xué)；基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：雷雨田20090514AbstractLetG∈Rn(n?3)beaboundedsimplyconnecteddomainwithsmoothboundary?G.DenoteSn?1=x∈Rn1:x21x22x23x2n=1.xn1=0Sn=x∈Rn1:x21x22x23x2n1=1.Letg=(g?0)beasmoot

2、hmapfrom?GintoSn?1satisfyingdeg(g??G)=d?=0.InthisdissertationwemainlystudytheconvergencepropertiesoftheregularizedminimizeruεofanenergyfunctionalEε(uG)=1n?G|?u|ndx12εn?Gu2n1dxonthefunctionclassW=u∈W1n(GSn):u|?G=g.InChapt

3、er1prefacewepresenttheconclusionsinthisdissertation.InChapter2weobtaintheLlestimateL∞estimatefthegradientofminimizers.InChapter3weusethegradientestimatesprovedinChapter2toprovetheC1αconvergenceofminimizers.InChapter4west