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PRODID:-//talks.bham.ac.uk//v3//EN
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CATEGORIES:Analysis seminar
SUMMARY:Non-autonomous maximal regularity for divergence-f
orm operators - Moritz Egert (UniversitÃ© Paris-Sud
)
DTSTART:20160321T160000Z
DTEND:20160321T170000Z
UID:TALK1936AT
URL:/talk/index/1936
DESCRIPTION:Let $V \\subseteq H$ be Hilbert spaces with dense
and continuous embedding. An old problem of J.L. L
ions asks for maximal regularity in $H$ of the non
-autonomous Cauchy problem \n$u'(t) + A(t) u(t) =
f(t)$\, $u(0) = 0$\,\nwhere each operator $A(t)$ i
s induced by an elliptic sesquilinear form on $V$.
Recent developments have carved out a threshold o
n the regularity of $A$ as a map $[0\,T] \\to \\ma
thcal{L}(V\, V^*)$: Lions' question can be answere
d in the affirmative in case of HÃ¶lder-continuity
of exponent $\\alpha > 1/2$ and there exist counte
rexamples if only $\\alpha < 1/2$. The borderline
case\, however\, was left open\, even if all opera
tors are differential operators in divergence-form
. In this talk we present a rather simple proof of
such a result stemming on some hidden coercivity
of the parabolic operator $\\partial_t + A$.
LOCATION:Lecture room B\, Watson building
CONTACT:Andrew Morris
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