By R. Glowinski, etc.

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**Example text**

In actual applications, a d i f f i c u l t y i n t h e implementation o f t h e above method r e s t s i n t h e e x p l i c i t calculation of t h e c o n j u g a t e f u n c t i o n @ * o f @. 16. A s l i g h t l y d i f f e r e n t approach i s given i n Cea 111, which i s a l s o v a l i d f o r nonsymmetric a ( u , v ) . See a l s o t h e a r t i c l e by Cea 121. 17. The f u n c t i o n @ i s given on V. We have i n t r o d uced t h e c o n j u g a t e f u n c t i o n on V ' . However, i d e n t i f y i n g V w i t h V ' , we' can also i n t r o d u c e the dual function on V.

7 ) , i . e . 8) u = S(u). c 1 ; i f f o r t h e moment we assume ( 3 . 9 ) t o be t r u e , t h i s g i v e s : ( i ) t h e e x i s t e n c e and uniqueness o f t h e s o l u t i o n 2 o f ( 3 . 10) b(u"+', u - u"") - p [ ~ ( u " tr, - u"") - (fi v - U"+')] >/ b(u", u - u"") VV E K and hence u " + u i n V . L e t us now v e r i f y ( 3 . 9 ) . 3) we can t a k e b(v, w ) t o be a new inner product i n V and t a k e II v II = (Nu, w2. We put wi = S(ui), i = 1, 2 and t a k e v = w2 ( r e s p . w l ) i n t h e i n e q u a l i t y ( 3 .

1 1 1 ) , on the cone of Hd(62) of functions 2 0. We p u t : A-' = G = Green's o p e r a t o r i n problem. 115) a r e given i n F u s c i a r d i , MOSCO, S c a r p i n t and S c h i a f f i n o 111. 15. In actual applications, a d i f f i c u l t y i n t h e implementation o f t h e above method r e s t s i n t h e e x p l i c i t calculation of t h e c o n j u g a t e f u n c t i o n @ * o f @. 16. A s l i g h t l y d i f f e r e n t approach i s given i n Cea 111, which i s a l s o v a l i d f o r nonsymmetric a ( u , v ) .