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SUMMARY:Thomas Stanin (University Salzburg)
DTSTART:20220125T170000Z
DTEND:20220125T180000Z
DTSTAMP:20260423T035032Z
UID:OSGA/94
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/94/">Gl
 obal continuity of variational solutions weakening the one-sided bounded s
 lope condition</a>\nby Thomas Stanin (University Salzburg) as part of Onli
 ne Seminar "Geometric Analysis"\n\n\nAbstract\nIn this talk\, we have a lo
 ok at regularity properties of variational solutions to a class of Cauchy-
 Dirichlet problems of the form\n\n$$\n\\begin{cases}\n\\partial_t u - \\ma
 thrm{div}_x (D_\\xi f(Du)) = 0 & \\text{in}\\ \\Omega_T\, \\\\\nu = u_0 & 
 \\text{on}\\ \\partial_\\mathcal{P}\\Omega_T.\n\\end{cases}\n$$\n\nWe do n
 ot impose any growth conditions from above on $f \\colon \\R^n \\to \\R$ b
 ut require it to be convex and coercive. The domain $\\Omega \\subset \\R^
 n$ is supposed to be bounded and convex and for the time-independent bound
 ary datum $u_0 \\colon \\overline\\Omega \\to \\R$\, we require continuity
 . These assumptions on $u_0$ are weaker than a one-sided version of the bo
 unded slope condition. We present a result showing variational solutions $
 u \\colon \\Omega_T \\to \\R$ to these problem class to be globally contin
 uous.\n
LOCATION:https://researchseminars.org/talk/OSGA/94/
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