The extension problem for fractional Sobolev spaces with a partial vanishing trace condition
Sign Up to like & getrecommendations! Published in 2021 at "Archiv der Mathematik"
DOI: 10.1007/s00013-021-01594-0
Abstract: We construct whole-space extensions of functions in a fractional Sobolev space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set $O$ which vanish in a suitable sense on a portion $D$ of… read more here.
Keywords: spaces partial; fractional sobolev; condition; problem fractional ... See more keywords
The extension problem of the mean curvature flow (I)
Sign Up to like & getrecommendations! Published in 2019 at "Inventiones mathematicae"
DOI: 10.1007/s00222-019-00893-2
Abstract: AbstractWe show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in $${{\mathbb {R}}}^3$$R3. read more here.
Keywords: mean curvature; curvature flow; extension problem; curvature ... See more keywords
A Liouville type theorem to an extension problem relating to the Heisenberg group
Sign Up to like & getrecommendations! Published in 2018 at "Communications on Pure and Applied Analysis"
DOI: 10.3934/cpaa.2018113
Abstract: We establish a Liouville type theorem for nonnegative cylindrical solutions to the extension problem corresponding to a fractional CR covariant equation on the Heisenberg group by using the generalized CR inversion and the moving plane… read more here.
Keywords: heisenberg group; type theorem; extension problem; liouville type ... See more keywords