2024 Tus sau: Elizabeth Oswald | [email protected]. Kawg hloov kho: 2024-01-13 00:07
Sobolev qhov chaw tau qhia los ntawm S. L. Sobolev nyob rau hauv lub lig 30s ntawm lub xyoo pua 20th. Lawv thiab lawv cov txheeb ze ua lub luag haujlwm tseem ceeb hauv ntau ceg ntawm lej: ib feem ntawm qhov sib npaug sib txawv, qhov muaj peev xwm xav tau, qhov sib txawv geometry, kwv yees txoj kev xav, kev tshuaj xyuas ntawm Euclidean qhov chaw thiab ntawm pawg dag.
Puas Sobolev qhov chaw ua tiav?
Hauv kev ua lej, qhov chaw Sobolev yog qhov chaw vector ntawm kev ua haujlwm nruab nrog cov qauv uas yog kev sib txuas ntawm Lp-cov qauv ntawm cov haujlwm ua ke nrog nws cov txiaj ntsig mus txog qhov muab xaj. Cov derivatives yog to taub nyob rau hauv ib tug haum tsis muaj zog kev txiav txim siab los ua tus chaw ua tiav, piv txwv li Banach chaw.
H1 qhov chaw yog dab tsi?
Qhov chaw H1(Ω) yog ib qhov chaw Hilbert sib cais. Pov thawj. Kom meej meej, H1 (Ω) yog qhov chaw ua ntej Hilbert. Let J: H1(Ω) → ⊕ n.
Qhov chaw H 2 yog dab tsi?
Rau qhov chaw ntawm cov haujlwm holomorphic ntawm qhov qhib chav disk, Hardy qhov chaw H2 muaj cov haujlwm f uas nws txhais tau tias tus nqi square ntawm lub voj voog ntawm lub voj voog r tseem bounded li r → 1 ntawm hauv qab no . Feem ntau, Hardy qhov chaw Hp rau 0 < p < ∞ yog chav kawm ntawm cov haujlwm holomorphic f ntawm qhov qhib chav tsev disk txaus siab.
Puas Sobolev qhov chaw sib cais?
Vim A(Wk, p(M)) yog isomorphic rau qhov chaw Wk, p(M), lub space Wk, p(M) yog sib cais.
Pom zoo:
Vim li cas txoj kev tseem ceeb tseem ceeb rau kev tswj xyuas qhov project?
txoj kev tseem ceeb tso cai rau pab pawg txheeb xyuas cov haujlwm tseem ceeb tshaj plaws hauv qhov project. … Qhov no muab kev nkag siab ntau dua rau koj qhov project ncua sij hawm thiab kev sib raug zoo ntawm cov haujlwm, ua rau koj nkag siab ntau ntxiv txog lub sijhawm ua haujlwm twg koj tuaj yeem hloov kho, thiab qhov twg yuav tsum nyob ib yam.
Vim li cas lub ntsiab lus tseem ceeb yog qhov tseem ceeb?
Grand mean centering sub lub ntsiab lus loj ntawm tus kwv yees siv qhov txhais los ntawm tag nrho cov qauv (X).. Vim li cas Grand txhais tau tias qhov chaw tseem ceeb? Lub ntsiab lus tseem ceeb yog qhov siv tau rov ntsuas duauas pab nrog kev txhais cov ntsiab lus cuam tshuam nrog kev cuam tshuam, nws txhais tau li cas, lossis qhov sib txawv ntawm txhua qib;
Puas yog qhov tseem ceeb lossis qhov tseem ceeb?
Emphasise thiab hais txog yog ob qhov kev hloov pauv ntawm cov lus qhia uas txhais tau hais tias qhov tseem ceeb ntawm qee yam. Keeb kwm, hais txog yog tus qauv hauv Askiv Askiv, tab sis niaj hnub no, kev hais qhia ntau dua hauv Askiv thiab Asmeskas Askiv.
Dab tsi yog qhov tseem ceeb thiab vim li cas nws tseem ceeb los txheeb xyuas koj qhov tseem ceeb?
Qhov tseem ceeb yuav coj koj hauv kev txiav txim siab hauv lub neej thiab ua rau koj taug qab. Qhov tseem ceeb tshaj plaws, qhov tseem ceeb tshaj plaws yuav ua rau koj ntseeg siab hais tias "tsis yog." Lawv pab koj txheeb xyuas qhov xav tau tiag tiag hauv koj lub neej, piv rau lwm tus xav tias tseem ceeb.
Vim li cas qhov tseem ceeb ntawm qhov muaj zog thiab qhov tsis muaj zog yog qhov tseem ceeb?
Nws yog ib qho tseem ceeb rau qhov tseem ceeb ntawm qhov ua tau zoo thiab qhov tsis muaj zog vim qhov no pab lub tuam txhab txiav txim siab txog thaj chaw uas lawv yuav tsum tau txhim kho ntxiv rau thaj chaw uas lawv ua tau zoo hauv. Vim li cas lub zog thiab qhov tsis muaj zog tseem ceeb?
