Derivation of Darcy’s law in randomly perforated domainsSpringer Science and Business Media LLC - Tập 60 - Trang 1-30 - 2021
A. Giunti
We consider the homogenization of a Poisson problem or a Stokes system in a randomly punctured domain with Dirichlet boundary conditions. We assume that the holes are spherical and have random centres and radii. We impose that the average distance between the balls is of size
$$\varepsilon $$
and ...... hiện toàn bộ
Finite time blow-up for the harmonic map heat flowSpringer Science and Business Media LLC - Tập 1 - Trang 231-236 - 1993
Joseph F. Grotowski
We consider the harmonic map heat flow from the three-dimensional ball to the two-sphere. We establish the existence of regular initial data leading to blow-up in finite time.
An improved Morse index bound of min–max minimal hypersurfacesSpringer Science and Business Media LLC - Tập 62 - Trang 1-32 - 2023
Yangyang Li
In this paper, we give an improved Morse index upper bound for minimal hypersurfaces from Almgren–Pitts min–max construction in any closed Riemannian manifold
$$M^{n+1}$$
$$(n+1 \ge 3$$
), which ge...... hiện toàn bộ
Asymptotic in Sobolev spaces for symmetric Paneitz-type equations on Riemannian manifoldsSpringer Science and Business Media LLC - Tập 35 - Trang 385-407 - 2008
Nicolas Saintier
We describe the asymptotic behaviour in Sobolev spaces of sequences of solutions of Paneitz-type equations [Eq. (E
α
) below] on a compact Riemannian manifold (M, g) which are invariant by a subgroup of the group of isometries of (M, g). We also prove pointwise estimates.
Some differentiable sphere theoremsSpringer Science and Business Media LLC - Tập 58 - Trang 1-24 - 2019
Qing Cui, Linlin Sun
In this paper, we obtain several new intrinsic and extrinsic differentiable sphere theorems via Ricci flow. For intrinsic case, we show that a closed simply connected
$$n(\ge 4)$$
-dimensional Riemannian manifold M is diffeomorphic to
...... hiện toàn bộ