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No C2,1 regularity for fully nonlinear parabolic equations
January 23rd, 2007 at 15:15 in HG G43 (HWZ)
Given by: Ulisse Stefanelli (IMATI Pavia & ETH)
Abstract:Locally bounded viscosity solutions to the fully nonlinear parabolic
equation ut=F(D2u) with F convex are known to be locally
C2,\alpha for some \alpha\in (0,1). The aim of this talk is to
show that C2,1 regularity is however not to be expected. We will
achieve this by considering a class of radially symmetric solutions to the
simplest fully nonlinear parabolic equation, namely
ut=max(\Delta u,\Delta u/2). In particular, we show that this equation admits solutions u such that \Delta u is not Lipschitz continuous.
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