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Optimal shape of a domain which minimizes the first buckling eigenvalue
Springer Science and Business Media LLC - Tập 55 - Trang 1-29 - 2016
In this paper we prove the existence of an optimal domain which minimizes the buckling load of a clamped plate among all bounded domains with given measure. Instead of treating this variational problem with a volume constraint, we introduce a problem without any constraints, but with a penalty term. We concentrate on the minimizing function and prove that it has Lipschitz continuous first derivati......
Derivation of Darcy’s law in randomly perforated domains
Springer Science and Business Media LLC - Tập 60 - Trang 1-30 - 2021
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 ......
Unstable extremal surfaces of the ?Shiffman-functional?
Springer Science and Business Media LLC - - 2004
Variations, approximation, and low regularity in one dimension
Springer Science and Business Media LLC - Tập 56 Số 3 - 2017
Finite time blow-up for the harmonic map heat flow
Springer Science and Business Media LLC - Tập 1 - Trang 231-236 - 1993
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.
Parabolic De Giorgi classes of order p and the Harnack inequality
Springer Science and Business Media LLC - Tập 26 - Trang 379-399 - 2006
We define suitable homogeneous parabolic De Giorgi classes of order p and show that in this context a Harnack inequality holds with a time gap of order ρ
p
.
An improved Morse index bound of min–max minimal hypersurfaces
Springer Science and Business Media LLC - Tập 62 - Trang 1-32 - 2023
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......
Asymptotic in Sobolev spaces for symmetric Paneitz-type equations on Riemannian manifolds
Springer Science and Business Media LLC - Tập 35 - Trang 385-407 - 2008
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.
Existence and multiplicity for elliptic p-Laplacian problems with critical growth in the gradient
Springer Science and Business Media LLC - Tập 57 Số 3 - 2018
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