pii-laplacian

ganitat, pii "-laplacian kinwa pii"-lapless operator haah haah kramacha ardhvartulakar lambvartulakar aanshik vibhedak operator aahe. heey laplas operatorche nonlinear generalization aahe, jithe sootra _ 1 laa sootra _ 2 varr shrenibaddha karanyachi parvanagi aahe. teey asey lihile jaate
jethe sootra _ 4 ashee paribhashit kelee aahe
vishesh prakaranat jevha sootra _ 6, haah operator nehamichya laplacianmadhye qamee hoto. pii"-laplaciancha samavesh asalelya samikarananchya sarvasadharan upayanmadhye shastriy arthane duyyam kram vyutpann nasatat, tyamule yaa samikarananche upay kamkuvat upay mhanoon samajoon ghetale pahijet. udaharanarth, aapan mhanato qee sobolev space sootra _ 7 chey karya 'yuu' heey eka kamkuvat upay aahe
jarr pratyek chachani karya sootra _ 9 sathee aamchyakade asel
jethe sootra _ 11 heey manak scalar utpadan darshavate.
urja rachana.
diriclate seema attins 'pii'-laplace samikaranache kamkuvat samadhan
kshetra sutramadhye _ 13 heey karyatmak urjeche laghookaran aahe.
sobolev space sutratil serve karyanmadhye _ 7 heey trace arthane seema atty purn karate. vishisht prakaranat sootra _ 16 aanee sootra _ 17 haah trijya 1 chaa chendu aahe, vareel samasyeche kamkuvat samadhan spashtapane mojale jaau shakate aanee asey dile jaate
jethe sootra _ 19 haah pariman sootra _ 20 aanee keval sootra _ 1 varr avalambun eka yogya sthirank aahe. 22 yaa sutrasathi shastriy arthane samadhan duppat bhinn nahee heey lakshat ghya.

