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1.3 compensated compactness

compensated compactness $B$O(B $B6u4V$NHF9] (K.N.Chueh, C.C.Conley and J.A.Smoller) $B$NITJQNN(B $B0h$NJ}K!$,$"$k$@$1$G!"$7$+$b$3$l$O$I$s$J>l9g$G$b40A4$JM-3&@-$r<($7$F(B $B$/$l$k$H$O8B$i$J$$!#$=$N$?$a!"(B[14] $B$G$b!"2r$NB8:_DjM}$G$O!"(B $B6a;w2r$,$b$70lMM$JM-3&@-$r;}$D$J$i$P!"$H$$$&I=8=$,$H$i$l$F$$$k$b$N$,(B $BB?$$!#(B

$B$=$l$KBP$7$F(B energy $BITEy<0$GJ]>Z$5$l$k(B $B$G$N(B $BM-3&@-$rMxMQ$G$-$J$$$+$H9M$($k$N$O<+A3$JJ}8~$G$"$k$,!"$3$N(B $B$K(B compensated compactness $B$r3HD%$9$k!"$H$$$&;n$_$O$9$G$K9T$o$l$F$$$k$h(B $B$&$G$"$k!#(B

M.Kruk [18],
P.Lin [19],
M.E.Schonbek [28],
J.Shearer [31],
Y.Zhou [39]

[28] (Schonbek) $B$,$=$N:G=i$N$h$&$G$"$j!"(BYoung measure $B$NDj(B $BM}$r(B $B$K3HD%$7$?(B Young measure $B$NDjM}$r=R$Y$F$$$k!#(B

[18] $B$d$3$3$K$O$"$2$F$$$J$$$$$/$D$+$NO@J8$G$=$N(B Young measure $B$,>\$7$/D4$Y$i$l$F$$$k$h$&$G$"$k!#(B

[39] $B$O(B compensated compactness $B$NDjM}$r(B $B$K3HD%$7$F$$$k(B $BJ*$i$7$/!"$3$l$bB>$N$$$/$D$+$NO@J8$G$b8&5f$5$l$F$$$k$i$7$$!#(B

[19], [31] $B$O$=$N(B compensated compactness $B$N7k(B $B2L$r(B [14] $B$NO@J8$G$O%+%P!<$5$l$F$$$J$$7A$N(B elasticity $B$NJ}(B $BDx<0$KE,MQ$7$F$$$kJ*$i$7$$!#(B