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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 their average
radius is $$\varepsilon ^{\alpha }$$ , $$\alpha \in (1; 3)$$ . We prove that, as
in the ...
Unstable extremal surfaces of the ?Shiffman-functional?
Springer Science and Business Media LLC - - 2004
On a K-component elliptic system with the Sobolev critical exponent in high dimensions: the repulsive case
Springer Science and Business Media LLC - Tập 56 Số 5 - Trang 1-51 - 2017
Study the following K-component elliptic system Here $$k\ge 2$$ is a integer and
$$\Omega \subset \mathbb {R}^N(N\ge 4)$$ is a bounded domain with smooth
boundary $$\partial \Omega $$ , $$a_i,\lambda _i>0$$ , $$b_i\ge 0$$ for all
$$i=1,2,\ldots ,k$$ and $$\beta <0$$ , $$2^*=\frac{2N}{N-2}$$ is the Sobolev
critical exponent. By the variational method, we obtain a nontrivial solution of
this system....
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 generalizes a result by Zhou (Ann
Math 192(3):767–820, 2020) for $$3 \le n+1 \le 7$$ . The novel techniques are
the construction of hierarchical deformations and a restrictive min–max theory.
These techniq...
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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