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(1)Problemes de régularité en optimisation de formes Tanguy Briançon. To cite this version: Tanguy Briançon. Problemes de régularité en optimisation de formes. Mathématiques [math]. Université Rennes 1, 2002. Français. �tel-00002013�. HAL Id: tel-00002013 https://tel.archives-ouvertes.fr/tel-00002013 Submitted on 25 Nov 2002. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(308)  † b 

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(310)         $ °^§ j³ N P ¯  !     1&5 U X“  1D5 RS‰ˆ¨5RS N 3×

(311) U Xàb 21 P R 

(312) "“X P 1 N l

(313) W

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(315) S 40 R 43Oˆ¨ W6 W

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(317) 5×X ¯ U X / X 5RS¤ /ON 1DS¤5RS¤® Ø

(318) t ’  45 U ¡X P 5  IX ¯ U X / X R5ST d3€40 VX5ST® § ¬ 21 b 1 P  1~1 N 365 /ON 540 1 / X U QON s

(319)   °{® N ST U !5R€0 N † 4¯ b O° a6§ 6³³Y§«S N 3×1 PJ//­N 1& ƒPt ’  1&5 U S / 1ˆYJST5 4ST 43J3J N 3 / P 5W 43—Õ0  P ST  ž40 V X U †b 4365“ƒ P ׈ OXˆ P 3J Ø6 bˆ¨ 21 

(320) P Ùb× 1 P R 1 1&5 X Q 1 N U P × 43

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(322) ؁° ^g§ j ³ § ÓÄX 

(323) S  ˆ P U 5J‚0 ‚X4Ô P  ‚JX3O1‚ˆ¨ / NQ U †¯ b ‚ 1&5×

(324) . N 365  † ؃ P  S¤36® 4 Y1D 4Ø 43

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(328) q’ X P ® N S‰1&ST3OXV 

(329) 1 /ON S¤365Y1o

(330) U X ê N 365S 4¯  ±

(331)   NP †3Oˆ N R ZR40 5 X Q U S¤ P 3J WbS¤3 N YX5S N 3I

(332) 1€ƒ P X365ST50 1   

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(335) L’  X ¯ U X ê N 365S 4¯  ë

(336) 3JS~ † b “Ä 1 / 40  † U Xd †0 V P U X ST5Z0 

(337)    1&S ,:ÖØJX3O1 U R0 ƒ P X5RS N 3  Ÿ P U 4 ±° ^§ h³ §Ÿ3b Ä 454ë N 3 / P 5o5 NP Ô NP Y1Ո  N S‰1DS¤ ’   ž  °3+س5 U ƒ P 6 ”•’  , ˜   3° +سÕX4® ˆ    X P 11DS~S¤ R J40 V P U ST 4 €ƒ P /ON 1R1&S Q §}fXS‰1   1D5 X U N Y1€1 N U P 5S N 3  P‚/ Nž Q U 4¯ b W6 à×S¤3JSTbST1X5RS N 3‚

(338) ê#N Rb WX1R1 N ˆ¨S†‚0 X ¯ " ,   ¡§O©X3O1 ˆ¨ Zˆ4X1W°^§eh³ 1D5 1X5S‰1 ê XST5 dX4® ˆ , Ö.°£X3O1 U  ˆ4X1€ 40 V P U ST 4 4ë U Wb 4 Q R “

(339) ZVX P ˆ  ¦6 b°^§eh³ 1D5¦ 4ÙXˆú5 4b †3

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(341) f 0 X3O1d5 NP 5 U Xf1 P S¤5R ‚ƒ P U  P U 5RS / U STˆ4X5R P o

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(343) ù /ON 5R~ ¯ 1& N 3 / P 5W X QON l N 365  † ƒ P ë1DS’  1&5 U S / 1ˆYJS¤5 4S¤ 433J ë X U N 1   1D5ZX ¯ / 40 STf 4¯ 5R  ‚vO3JSÎJX3O1 +ק ª NP Ô NP Y1€X4® ˆ€ˆ¨ †55 6ù /ON 5R~ ¯ 1D ë U N Y1Rƒ P ’  21&5 U S / 1Rˆ S¤5 †S¤ 43J3 ! 45 /­N 1&ST5S¤® ëS U 1D5 /ON 11&S Q U  ¡X QON Y6 4 U 21!5 ˆYJ3JS„ƒ P 21€ 4Ù / U N 1&S N 3 /ONP W R 4VX Y

(344) 4 JX ¯ U X U NP/  U “ˆ N  /ON R5 4b †3

(345) 5‘

(346) U X¦1 N U P 5S N 3‚X P ® N S‰1DS¤3OXV 

(347) 1 /ON S¤365Y1! PbQON Y1¨ëOˆ 1&5X¦¯ 6S¤  U ¦ˆ N  /ON R5 4× 43

(348) 5Ճ P X3² ¦5 †3Or® 4 1€Ös6 G’  ° "³ ,  ’~° " ž – "³ N P ¯ ’~° " ž ³ , Ö

(349) § ¬  1&5ˆ¨ dƒ P d3 NP 1 ê XS‰1 N 3O1WX P ˆYOX / S¤5 R d6ë N P ¯ 3 NP 1 N 365 N 3O1 U 1 ˆ N 36® 4 RV 43Oˆú 1 3±20 ˆ¨ 11RXST  1~ 45 N P ¯ 3 NP 1oՆ0 VXV N 3²1 U 21 / N/ RS†40 50 1

(350) U X U STbS¤5R ’ ž §Ÿ3 / X 5RS‰ˆ P U S¤ 4 †ë 3 NP 1S„

(351) 4365eS v N 3O1 ˆ N  / U 4¯ 5R 4Ø 43

(352) 5 U X U S¤bST5P ’ ž 1DS " ž 1D5 P 3 /­N S¤365W

(353) U X ê N 365S †¯  0  P ST5 Z°{® N ST U “5±0 N † †¯ b “6§ a³Y§­ 3‚ N 3

(354) 5R  XS¤3²1&S΃ P  N 3‚X¦ 4ÙXˆ¨5R 4b 4365€° b 1D5 U X 3 N ‚X U W6   43 " ž ³ ’ ž #° "³ , 6

(355)  þ°   "³ÕJX3O1 U Z

(356) 4bSÄ 1 / Xˆ¨  "   $:Ö $Ø 45 ’ #° "³ ,-ւ1 P U ¡X P 5 R d

(357) 4×eS d 1 / Xˆ¨ ë N P ¯ ¼X /J/ X YX & 5ZJX3O1d ° ^e§ h³Y§~‡ S¤3O1DS

(358)  ¼ 1&5 U X¦ž ®X U P 

(359) U Xdˆ N 3O1&5 X365 :X /J/ X YXS‰1R1X365WJX3O1W° ^§  ³ §  X ˆ¨ ZXW ¯ ˆ¨ 455R €S‰

(360) †3

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(363) ëJS U 4Ù

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(365) ê XS¤  Ø6 1 / † 5 P Q X5S N 3O1¦6   ƒ P SÕ

(366) S¤bST3 P 43

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(368) 1Ճ P X365S¤50 1   

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(370) q’ ÄX ¯ U X ê N 365S 4¯  W 45 U ê XS¤5 ê#N 3OJXb 4365YX U /ONP 3 N 5 R / NQ U 4¯ b Iƒ P     °#       ³ , Ö

(371) § Ÿ3,vO3þëÉV X ˆ¨ X ¯ U  S¤3²

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(373) 21 4Ù / U N 1&S N 3O1X P ® N S„1&ST3OXV Ø

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(375)  ”t’  –˜1™ #  / X Ï X /J/ON 5WX ¯  !     ° X P 1& 43²1Ï6 1b 1 P  1Î

(376) ¥X N 3³Î®X P 5

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(378) 5 U  S„

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(380) 5 U 21 0 1 P U 5 X5 1

(381) ' )‘1 P U Xs 40 V P U X RS¤5Z0 

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(383) ^¨.  wr — ‚

(384) ‚  . 

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(400) o  / N  P ST  oS¤365†0 V YX U 4× 43

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(402) / 43O1& † ؃ P  43ž

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(406) R U 1Ï5R ˆYJ3JS‰ƒ P 1‘

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(410) 5RS‰ƒ P W1¨ 43I!0  P S¤54§ Ò 3J “ƒ P 1D5S N 3‚ƒ P S 21&5€ˆú 4 5 XS¤3 4b 4365 / U P 1Õ

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(413) U X ê N 365S 4¯   4 b € †3‚

(414) S¤× 43O1&S N 3‚6§O N 5 N 3O1€ƒ P ZJX3O1 U  4Ù

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(416) 5RS£ 4¯ R U S Q  

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(418) S¤b †3O1&S N 3¼

(419) P Ùë U X ê N 3

(420) 5RS£ 4¯ R U S Q R x’ ÑÖ $‚ 1&5 X3OX U ù65S‰ƒ P I°{‚XS‰1 / X1 /­NP  x’ ,:. Ö $³ § ¥€ 1D5 b‚XS¤365 43²X365 U / NQ U †¯ b bˆ N  / U 45d ° ^c§ ^³WX4® ˆ U b5R 4 × dV0 N µ40 5 RS‰ƒ P 1>=Z°  $?+س $ 1 BÖ6§å 3 / P 5 / 43O1D 4 Zƒ P dˆ¨ d5R 4 b W 1D5“ 43Oˆ N  / U P 1 40 V P U X RS‰1RX365 45o1¨ X5R5 43O6   N 3OˆZX ¯ P 3J ê N 365S †¯  / U P 1å †0 V P U S£ 4¯ R § ÓO 5 X4®XS U R 1&5R dX ¯ ê XS¤  § NP 1 X2® N 3O1€1& P U 4× 43

(421) 5‘ YX1R1& 4 Q U “0 JX3O1 ˆ¨ 455R “6 4 3JS 4¯  / X R5S¤ Œƒ P U ƒ P 1!ˆ N 365 S QJP 5RS N 3²1 45΃ P U ƒ P 1O  4‚X Yƒ P 1OJX3O1åˆú 455R o

(422) S¤ R ˆ¨5RS N 3þ§4 NP 1~X4® N 3O1ÎX P 1R1&S6Ն0 5YXS U¤U o0 ƒ P U ƒ P 1 X /J/ N ˆ  1å 43 

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