Control and Information Sciences

Lecture Notes in Control and Information Sciences ~~

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.J..i1­ m Fn:RENTl ll TI ON ON 11 LI «scur, i:: MAN IFOl.1l

J a cques Si'lL"n

Analysa ~u m 6 r i q u e . Tour 55- 6 5, 5e 0 t oge

Univ cr s it ': Pier r e e t Ha r Le Cur Le

4 Place Ju s 91 " ;L. 7 S2 52 Pllitl S CEDEX 05

I N T R() ll ll C 'l'JIl~

Edited by M.Thoma and A. Wyner

Le t l' 1>" a man If o l d of It

s c n t In g the vu r Ia t I ous of t hc 1I111 n l£ o l d . The t r a n s po r t c d ",o n i( o l d 1~

xE r]

r ov " Ix + v(x):

u~

IFIP

N anll let v be a vec tor field \l efi ncJ In a ll of I: N r l.'pre­

A function ~ ba i n~ g i v e n in a l l of ~N.

114

IoIC ~ r c Int cr c s eed

",It'h l, ~ ,,;,, '(:t lO the vu c Io t tons of I', Jf a l I '~i

A. Bermudez (Editor)

in th e var in t i on a of

f1,,,

no Lds ,

fI'.v ~ ,:,) . J n

L~

x

S tis

r+v

t hc du t a ar e s mooth eno u g h the fo11o­

cx p "~ n :;io n

whe r e v

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280

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r

Til "IlIU:H, Let

let f € LI (r) be such t ha t , fot" every ma p "G, f . 1:) C f E Ill, I (1'),

.

Th " n 'J (f ."G) E l.I (0

n.

f ~

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....h l ry v al ue pr o b l e ms s u c h as t he dr ab o f a bod y. Ilo re g c n u r a l.l y the d If f o r cn rra I c a lcu l u s On ma n ifo l d s ,;It ll c o r n u r s may be u s uf u I in a lot of p ro bl ems , Jt r cna l n s to g Iv e t he f ull p r ov e " , vh Ich re q u Lr o

0

f ull bo o k .

~ E F E R F.t{CF. S

HIJl(,\T F . , SI HON 1'1Ih 1. of !':l rls

Differential ge ometry , Van Nos t ra n d .

ZOI.l : SIO

All t he terms of t he e xpans Io n a r c de fln CfI. In d e ed

I

H. (1974).

J. ( 197(,) . Su r 1 " c o n t r ole pa r lin dO" r ~lin e l: ~ o " I ':: t r l