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Extra info for (0, 1, 2, 4) Interpolation by G -splines

Example text

55) I (r, u) I

9). 21) inf J(u) , ,u E K . 22) -':,;{! u) ( L o - u) VUEK. 22)is an elasto-plasticity problem. 3 admits a unique solution. 4 The problem can be interpreted as follows ( 2 ) : the open domain R consists of two regions and 62, (the elastic region and the plastic region, respectively). g. Lanchon / 2 / , Glowinski-Lanchon /l/). (2) This will be dealt with in more detail in Chapter 3. Examples (SEC. 24) 1 . t o which we add: u = O on and some t r a n s m i s s i o n c o n d i t i o n s which i n c i d e n t a l l y a r e somewhat awkward t o e x p r e s s e x p l i c i t l y ( s e e Br6zis 111) - a t t h e i n t e r f a c e between Sl, and a,,.

113) VUEK, and hence i s e q u i v a l e n t t o f i n d i n g the projection of $ , i n the sense of the inner product ( 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 @.

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