Yog sobolev qhov chaw sib cais?

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 L^p-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 H^{p rau 0 < p < ∞ yog chav kawm ntawm cov haujlwm holomorphic f ntawm qhov qhib chav tsev disk txaus siab.}