BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Sabre//Sabre VObject 4.6.0//EN
CALSCALE:GREGORIAN
BEGIN:VTIMEZONE
TZID:Europe/Zurich
X-LIC-LOCATION:Europe/Zurich
TZURL:http://tzurl.org/zoneinfo/Europe/Zurich
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:19810329T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:19961027T030000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:news464@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181228T174506
DTSTART;TZID=Europe/Zurich:20150429T151500
SUMMARY:Seminar Analysis: Bernard Dacorogna (EPFL)
DESCRIPTION:Given two functions f and g\,we want to find a map φ such tha
 t\\r\\ng(φ(x)) det∇φ(x)=f(x)   x∈Ω\,              
      φ(x)=x       x∈∂Ω.\\r\\nLocal case. We first consider 
 the (local) existence\, uniqueness and optimal regularity for the problem\
 \r\\ngi(φ(x)) det∇φ(x)=fi(x)  for every 1≤i≤n\\r\\nwhere gi·fi>0
 .\\r\\nGlobal case. A necessary condition is then\\r\\n∫Ω f =∫Ω g. 
                             (1)\\r\\n(i) We dis
 cuss the case where g·f>0 and give three different ideas for the existenc
 e problem with optimal regularity.\\r\\n(ii) We then briefly comment on th
 e case where g>0 but f is allowed to change sign.\\r\\nA problem without t
 he condition (1). We consider a more general problem of the form\\r\\n  
           det∇φ(x)=f(x\,φ(x)\,∇φ(x))   x∈Ω\,    
                φ(x)=x                        
 x∈∂Ω.\\r\\nwhere no constraint of the type (1) is needed.
X-ALT-DESC:\nGiven two functions f and g\,we want to find a map&nbsp\;φ su
 ch that\ng(φ(x)) det∇φ(x)=f(x)&nbsp\;&nbsp\; x∈Ω\,<br />&nbsp\;&nbs
 p\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&
 nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\; φ(x)=x&nbsp\;&nbsp\;&nbsp\; &nb
 sp\;&nbsp\; x∈∂Ω.\nLocal case. We first consider the (local) existenc
 e\, uniqueness and optimal regularity for the problem\ng<sub>i</sub>(φ(x)
 ) det∇φ(x)=f<sub>i</sub>(x)&nbsp\; for every 1≤i≤n\nwhere g<sub>i</
 sub>·f<sub>i</sub>&gt\;0.\n<i>Global case</i>. A necessary condition is t
 hen\n∫<sub>Ω</sub> f =∫<sub>Ω</sub> g. &nbsp\;&nbsp\;&nbsp\;&nbsp\;&
 nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp
 \;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&n
 bsp\;&nbsp\; (1)\n(i) We discuss the case where g·f&gt\;0 and give three 
 different ideas for the existence problem with optimal regularity.\n(ii) W
 e then briefly comment on the case where g&gt\;0 but f is allowed to chang
 e sign.\n<i>A problem without the condition (1)</i>. We consider a more ge
 neral problem of the form\n&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp
 \;&nbsp\;&nbsp\;&nbsp\;&nbsp\; det∇φ(x)=f(x\,φ(x)\,∇φ(x))&nbsp\;&nb
 sp\; x∈Ω\,<br />&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\
 ;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\; φ
 (x)=x&nbsp\;&nbsp\;&nbsp\;&nbsp\; &nbsp\; &nbsp\; &nbsp\; &nbsp\; &nbsp\; 
 &nbsp\; &nbsp\;&nbsp\; &nbsp\; &nbsp\; x∈∂Ω.\nwhere no constraint of 
 the type (1) is needed.\n\n
DTEND;TZID=Europe/Zurich:20150429T161500
END:VEVENT
END:VCALENDAR