共查询到20条相似文献,搜索用时 31 毫秒
1.
Let be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ?Ω. We show that the solution to the linear first-order system:(1) vanishes if and . In particular, square-integrable solutions ζ of (1) with vanish. As a consequence, we prove that: is a norm if with , for some with as well as . We also give a new and different proof for the so-called ‘infinitesimal rigid displacement lemma’ in curvilinear coordinates: Let , , satisfy for some with . Then there exists a constant translation vector and a constant skew-symmetric matrix , such that . 相似文献
2.
Petru Mironescu 《Comptes Rendus Mathematique》2010,348(13-14):743-746
3.
Zhiqiang Xu 《Applied and Computational Harmonic Analysis》2018,44(2):497-508
The paper presents several results that address a fundamental question in low-rank matrix recovery: how many measurements are needed to recover low-rank matrices? We begin by investigating the complex matrices case and show that generic measurements are both necessary and sufficient for the recovery of rank-r matrices in . Thus, we confirm a conjecture which is raised by Eldar, Needell and Plan for the complex case. We next consider the real case and prove that the bound is tight provided . Motivated by Vinzant's work [19], we construct 11 matrices in by computer random search and prove they define injective measurements on rank-1 matrices in . This disproves the conjecture raised by Eldar, Needell and Plan for the real case. Finally, we use the results in this paper to investigate the phase retrieval by projection and show fewer than orthogonal projections are possible for the recovery of from the norm of them, which gives a negative answer for a question raised in [1]. 相似文献
4.
In a previous work, it was shown how the linearized strain tensor field can be considered as the sole unknown in the Neumann problem of linearized elasticity posed over a domain , instead of the displacement vector field in the usual approach. The purpose of this Note is to show that the same approach applies as well to the Dirichlet–Neumann problem. To this end, we show how the boundary condition on a portion of the boundary of Ω can be recast, again as boundary conditions on , but this time expressed only in terms of the new unknown . 相似文献
5.
Anton Alekseev Nariya Kawazumi Yusuke Kuno Florian Naef 《Comptes Rendus Mathematique》2017,355(2):123-127
We define a family of Kashiwara–Vergne problems associated with compact connected oriented 2-manifolds of genus g with boundary components. The problem is the classical Kashiwara–Vergne problem from Lie theory. We show the existence of solutions to for arbitrary g and n. The key point is the solution to based on the results by B. Enriquez on elliptic associators. Our construction is motivated by applications to the formality problem for the Goldman–Turaev Lie bialgebra . In more detail, we show that every solution to induces a Lie bialgebra isomorphism between and its associated graded . For , a similar result was obtained by G. Massuyeau using the Kontsevich integral. For , , our results imply that the obstruction to surjectivity of the Johnson homomorphism provided by the Turaev cobracket is equivalent to the Enomoto–Satoh obstruction. 相似文献
6.
Qiyu Sun 《Applied and Computational Harmonic Analysis》2012,32(3):329-341
In this paper, it is proved that every s-sparse vector can be exactly recovered from the measurement vector via some -minimization with , as soon as each s-sparse vector is uniquely determined by the measurement z. Moreover it is shown that the exponent q in the -minimization can be so chosen to be about , where is the restricted isometry constant of order 2s for the measurement matrix A. 相似文献
7.
8.
This paper deals with the following nonlinear elliptic equation where , is a bounded non-negative function in . By combining a finite reduction argument and local Pohozaev type of identities, we prove that if and has a stable critical point with and , then the above problem has infinitely many solutions. This paper overcomes the difficulty appearing in using the standard reduction method to locate the concentrating points of the solutions. 相似文献
10.
11.
12.
13.
14.
Existence of standing waves of nonlinear Schrödinger equations with potentials vanishing at infinity
Ohsang Kwon 《Journal of Mathematical Analysis and Applications》2012,387(2):920-930
For a singularly perturbed nonlinear elliptic equation , , we prove the existence of bump solutions concentrating around positive critical points of V when nonnegative V is not identically zero for or nonnegative V satisfies for . 相似文献
15.
Zuoshunhua Shi 《Journal of Differential Equations》2018,264(3):1550-1580
In this paper, we mainly study the existence of self-similar solutions of stationary Navier–Stokes equations for dimension . For , if the external force is axisymmetric, scaling invariant, continuous away from the origin and small enough on the sphere , we shall prove that there exists a family of axisymmetric self-similar solutions which can be arbitrarily large in the class . Moreover, for axisymmetric external forces without swirl, corresponding to this family, the momentum flux of the flow along the symmetry axis can take any real number. However, there are no regular () axisymmetric self-similar solutions provided that the external force is a large multiple of some scaling invariant axisymmetric F which cannot be driven by a potential. In the case of dimension 4, there always exists at least one self-similar solution to the stationary Navier–Stokes equations with any scaling invariant external force in . 相似文献
16.
17.
18.
19.