简介:LetMbeanndimensionalcompleteRiemannianmanifoldsatisfyingthedoublingvolumepropertyandanon-diagonalheatkernelestimate.Thenecessary-sufficientconditionfortheSobolevinequality‖f‖q≤Cn,,v,p,q(‖▽f‖p+‖fp)(2≤p<q<∞)isgiven.
简介:Anewhigh-ordertime-steppingfiniteelementmethodbaseduponthehigh-ordernumericalintegrationformulaisformulatedforSobolevequations,whosecomputationsconsistofaniterationprocedurecoupledwithasystemoftwoellipticequations.Theoptimalandsuperconvergenceerrorestimatesforthisnewmethodarederivedbothinspaceandintime.Also,aclassofnewerrorestimatesofconvergenceandsuperconvergenceforthetime-continuousfiniteelementmethodisdemonstratedinwhichtherearenotimederivativesoftheexactsolutioninvolved,suchthattheseestimatescanbeboundedbythenormsoftheknowndata.Moreover,someusefula-posteriorierrorestimatorsaregivenonthebasisofthesuperconvergenceestimates.
简介:TheauthorsstudythesingularintegraloperatorTΩ,αf(x)=p.v.∫R^nb(|y|Ω(y′)|y|^-n-αf(x-y)dy,definedonalltestfunctionsf,wherebisaboundedfunction,α>0,Ω(y′)isanintegrablefunctionontheunitsphereS^n-1satisfyingcertaincancellationconditions.Itisprovedthat,forn/(n+α)<p<∞,TΩ,αisaboundedoperatorfromtheHardy-SobolevspaceH^pαtotheHardyspaceH^p.TheresultsanditsapplicationsimprovesometheoremsinapreviouspaperoftheauthorandtheyareextensionsofthemaintheoremsinWheeden'spaper(1969).TheproofisbasedonanewatomicdecompositionofthespaceH^pαbyHan,PaluszynskiandWeiss(1995).Byusingthesameproof,thesingluarintegraloperatorswithvariablekernelsarealsostudied.
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简介:Inthispaper,weconsiderthen-widthsandaveragewidthsofBesovclassesintheusualSobolevspaces.TheweakasymptoticresultsconcerningtheKolmogorovn-widths,thelinearn-widths,theGel'fandn-widths,intheSobolevspacesonT~d,andtheinfinite-dimensionalwidthsandtheaveragewidthsintheSobolevspacesonR~dareobtained,respectively.
简介:ThediscreteSobolev’sinequalitiesinL_pnormareprovedforthree-dimensionalsphericalandcylindricalcoordinates,byusingdiscreteHolderinequality.propertyofthetrianglefunctionsandcomplicateddeduction.
简介:Theinverseheatconductionproblem(IHCP)isaseverelyill-posedprobleminthesensethatthesolution(ifitexists)doesnotdependcontinuouslyonthedata.Butnowtheresultsoninverseheatconductionproblemaremainlydevotedtothestandardinverseheatconductionproblem.SomeoptimalerrorboundsinaSobolevspaceofregularizedapproximationsolutionsforasidewaysparabolicequation,i.e.,anon-standardinverseheatconductionproblemwithconvectiontermwhichappearsinsomeappliedsubjectaregiven.
简介:Inthispaper,westudyoptimalrecovery(reconstruction)offunctionsonthesphereintheaveragecasesetting.WeobtaintheasymptoticordersofaveragesamplingnumbersofaSobolevspaceonthespherewithaGaussianmeasureintheLd-1q(S)metricfor1≤q≤∞,andshowthatsomeworst-caseasymptoticallyoptimalalgorithmsarealsoasymptoticallyoptimalintheaveragecasesettingintheLdq(S-1)metricfor1≤q≤∞.
简介:分算法(静止或非静止)是在小浪的最活跃、令人激动的研究话题之一分析和应用数学理论。处于多维的非静止的状况,它的限制功能简洁地两个都被支持并且无穷地可辨。另外,这些限制功能能用作可伸缩的功能产生多维非静止直角或biorthogonalsemi-multiresolution分析(Semi-MRAs)。光谱多维的nonstationarybiorthogonalSemi-MRAs的近似性质在这篇论文被考虑。基于放大函数的nonstationary分计划和它的限制,多维的nonstationarybiorthogonalSemi-MRAs有,这被显示出光谱在Sobolev空格H的近似顺序r[s](R[d]),为所有rs0。[从作者抽象]