2024 Tus sau: Elizabeth Oswald | [email protected]. Kawg hloov kho: 2024-01-13 00:07
Vim A(Wk, p(M)) yog isomorphic rau qhov chaw Wk, p(M), lub space Wk, p(M) yog sib cais.
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.
Vim li cas Sobolev qhov chaw tseem ceeb?
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.
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.
Pom zoo:
Dab tsi yog qhov sib txawv ntawm kev sib cais thiab txuas ntxiv?
Discrete cov ntaub ntawv yog cov ntaub ntawv uas tuaj yeem coj qee qhov txiaj ntsig. … Cov ntaub ntawv tsis tu ncua yog cov ntaub ntawv uas tuaj yeem coj tus nqi. Qhov siab, qhov hnyav, qhov kub thiab qhov ntev yog txhua yam piv txwv ntawm cov ntaub ntawv txuas ntxiv.
Puas yog qhov sib faib lossis sib cais?
Cov lus qhia compartmentalize yog los ntawm noun compartment, nws tus kheej los ntawm Fabkis Qub compartiment, "partitioned off," los ntawm Late Latin compartiri, "rau faib." "Koj tsis tuaj yeem faib koj lub neej zoo li no!
Puas yog qhov chaw ua si dutton yog qhov chaw zoo?
Kuv kev tshuaj xyuas tsis yog kev qhuas raws li kuv qhov kev paub nrog Dutton Park tau ua rau muaj kev tsis txaus siab thiab kev thab plaub hauv zej zog. … Thiab ntawm kev pheej hmoo ntawm kev txo qis ntawm kuv tus kheej cov khoom muaj nqis Kuv tsis tuaj yeem ua lub siab zoo pom zoo rau lub nroog no tshwj tsis yog tias koj tsis yog cov ilk los pab txhawb rau zej zog raws kev thab plaub.
Kev tsis sib xws hauv qhov chaw sobolev?
Cov no yog siv los ua pov thawj Sobolev embedding theorem, muab suav nrog ntawm qee qhov chaw Sobolev, thiab Rellich-Kondrachov theorem qhia tias nyob rau hauv cov xwm txheej muaj zog me ntsis qee qhov Sobolev yog compactlyembedded hauv lwm tus.
Thaum lub sijhawm ntsuas qhov sib npaug ntawm qhov ntsuas cua sov yog nyob rau hauv kev sib cais?
Los ntawm txoj cai thib ob ntawm thermodynamics: Txoj cai thib ob ntawm thermodynamics hais tias qhov entropy ntawm ib qho cais qhov system yeej tsis txo qis, vim tias cov tshuab cais ib txwm hloov mus rau qhov sib npaug ntawm qhov ntsuas kub, lub xeev nrog siab kawg entropy.
