earling yokka lemma

ganitamlo, simhaala lemma anie kooda piluvabade earling lemma, banach pradaesaalaku sambandhinchina phalitam. idhi tarachugaa sobolev pradaesaalaloo konni nibandhanala samaanatvaanni pradarsinchadaaniki kriyaatmaka vislaeshanhaloo upayoginchabadutundi. dheeniki gunnar earling paeru pettaru.
lemma yokka prakatana.
lett ("x", ||·||"x"), ("y", ||·||"y") mariyu ("" z ","  ||·||"z") moodu banach pradaesaalu. ilaa anukundam
appudu, prati "ε"> "ε">, oka sthiraamkam "c" ("ε") untundi, antey, anni "x" ω "x" kii,
corolary (sobolev pradaesaalaku samaanamaina nibandhanalu).
ωr "n" terichi mariyu sarihaddulugaa undanivvandi, mariyu "k" ωn gaa undanivvandi. sobolev space "h" k "(ω)" h "k" −1 (ω) loe compactga ponduparachabadindani anukundam. appudu "h" k "(ω) paie eee krindi rendu nibandhanalu samanamga untayih
mariyu
sunna trace (ω yokka sarihaddulo sunna ayinavi) thoo kuudina sobolev functionlatho kuudina "h" k "(ω) yokka upasthaanaaniki," u "yokka" l "2 pramaanaanni maroka samaanamaina pramaanaanni ivvadaaniki vadiliveyavacchu.

