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Microscopic renormalized energy for a pinned Ginzburg–Landau functional
Springer Science and Business Media LLC - Tập 53 - Trang 65-89 - 2014
We study the vortex location for minimizers of a Ginzburg–Landau energy with a discontinuous constraint. The discontinuous constraint appears in the potential
$$(a^2-|u|^2)^2$$
. The function
...... hiện toàn bộ
Green’s function for elliptic systems: existence and Delmotte–Deuschel bounds
Springer Science and Business Media LLC - Tập 56 - Trang 1-51 - 2017
This paper is divided into two parts: In the main deterministic part, we prove that for an open domain
$$D \subset \mathbb {R}^d$$
with
$$d \ge 2$$
...... hiện toàn bộ
Homogenization of Steklov eigenvalues with rapidly oscillating weights
Springer Science and Business Media LLC - Tập 61 - Trang 1-19 - 2022
In this article we study the homogenization rates of eigenvalues of a Steklov problem with rapidly oscillating periodic weight functions. The results are obtained via a careful study of oscillating functions on the boundary and a precise estimate of the
$$L^\infty $$
bound of eigenfunctions. As an...... hiện toàn bộ
A negative answer to a one-dimensional symmetry problem in the Heisenberg group
Springer Science and Business Media LLC - - 2003
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
Sharp Rellich-Leray inequality for axisymmetric divergence-free vector fields
Springer Science and Business Media LLC - Tập 58 - Trang 1-23 - 2019
In this paper, we show the N-dimensional Rellich-Leray inequality with optimal constant for axisymmetric and divergence-free vector fields. This is a second-order differential version of the former work by Costin-Maz’ya (Calc Var Partial Differ Equ 32(4):523–532, 2008) on sharp Hardy–Leray inequality for such vector fields. In the proof of our main theorem, we show the vanishing of azimuthal compo...... hiện toàn bộ
Compactness for a class of integral functionals with interacting local and non-local terms
Springer Science and Business Media LLC - Tập 62 - Trang 1-28 - 2023
We prove a compactness result with respect to
$$\Gamma $$
-convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the
...... hiện toàn bộ
A combinatorial Yamabe problem on two and three dimensional manifolds
Springer Science and Business Media LLC - Tập 60 - Trang 1-45 - 2021
In this paper, we define a new discrete curvature on two and three dimensional triangulated manifolds, which is a modification of the well-known discrete curvature on these manifolds. The new definition is more natural and respects the scaling exactly the same way as Gauss curvature does. Moreover, the new discrete curvature can be used to approximate the Gauss curvature on surfaces. Then we study...... hiện toàn bộ
Curvature bounds by isoperimetric comparison for normalized Ricci flow on the two-sphere
Springer Science and Business Media LLC - Tập 39 - Trang 419-428 - 2010
We prove a comparison theorem for the isoperimetric profiles of solutions of the normalized Ricci flow on the two-sphere: If the isoperimetric profile of the initial metric is greater than that of some positively curved axisymmetric metric, then the inequality remains true for the isoperimetric profiles of the evolved metrics. We apply this using the Rosenau solution as the model metric to deduce ...... hiện toàn bộ
Effective multiplicity for the Einstein-scalar field Lichnerowicz equation
Springer Science and Business Media LLC - - 2015
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