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. … Lawv muaj npe tom qab Sergei Lvovich Sobolev.
Puas Sobolev chaw ua tiav?
Sobolev chaw yog qhov chaw vector ntawm kev ua haujlwm nruab nrog cov qauv uas yog kev sib txuas ntawm cov qauv ntawm kev ua haujlwm nws tus kheej nrog rau nws cov derivatives mus txog qhov kev txiav txim. Cov derivatives yog to taub nyob rau hauv ib tug haum tsis muaj zog kev txiav txim siab los ua qhov chaw tiav, yog li Banach chaw.
Puas Sobolev chaw Banach chaw?
Sobolev qhov chaw uas tsis yog tus lej k
Lawv are Banach qhov dav dav thiab Hilbert qhov chaw tshwj xeeb p=2.
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.
Yog Sobolev qhov chaw hloov pauv?
Cov chaw Sobolev, ib yam li Lp chaw, yog reflexive thaum 1<p<∞.
