作者机构：
[Deng Qingquan; Yao Xiaohua] Department of Mathematics, Central China Normal University;[Ding Yong] School of Mathematical Sciences, Beijing Normal University
关键词：
Global Science Press;ATA;Analysis in Theory and Applications;Higher order Schrödinger operator;off-diagonal estimates;HpL spaces;area integrals.
摘要：
Let L = L0 ＋ V be the higher order Schrodiger type operator where L0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coeffi- cients and V is a real measurable function as multiplication operator （e.g., including （-△）m＋v （m∈N） as special examples）. In this paper, assume that V satisfies a strongly subcritical form condition associated with L0, the authors attempt to establish a the- HL （R） （0 〈 p ≤ 1） associated with the higher order Schrodinger ory of Hardy space P n type operator L. Specifically, we first define the molecular Hardy space Hp （JRn） by the so-called （p, q,ε, M） molecule associated to L and then establish its characterizations by the area integral defined by the heat semigroup e-tL.
作者机构：
[Guo, Jun] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.;[Fan, Lili] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China.;[Yan, Guozheng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Fan, Lili] W;Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China.
关键词：
Boundary integral equation;Helmholtz equation;Fredholm theory
摘要：
We consider a kind of scattering problem by a crack Γ that is buried in a bounded domain D, and we put a point source inside the domain D. This leads to a mixed boundary value problem to the Helmholtz equation in the domain D with a crack Γ. Both sides of the crack Γ are given Dirichlet-impedance boundary conditions, and different boundary condition (Dirichlet, Neumann or Impedance boundary condition) is set on the boundary of D. Applying potential theory, the problem can be reformulated as a system of boundary integral equations. We establish the existence and uniqueness of the solution to the system by using the Fredholm theory.
摘要：
We consider the inverse scattering problem of determining the shape of a thin dielectric infinite cylinder having an open arc as cross section. Assuming that the electric field is polarized in the TM mode, this leads to a mixed boundary value problem for the Helmholtz equation defined in the exterior of an open arc in R~2. We suppose that the arc has mixed Dirichlet-impedance boundary condition, and try to recover the shape of the arc through the far field pattern by using the factorization method. However, we are not able to apply the basic theorem introduced by Kirsch to treat the far field operator F, and some auxiliary operators have to be considered. The theoretical validation of the factorization method to our problem is given in this paper, and some numerical results are presented to show the viability of our method.
作者机构：
[Dong, Cai-lin] Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhou, Jie; Sun, Liu-quan] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China.;[Zhou, Jie] Capital Normal Univ, Sch Math, Beijing 100048, Peoples R China.
通讯机构：
[Sun, Liu-quan] C;Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China.
摘要：
Case-cohort sampling is a commonly used and efficient method for studying large cohorts.In many situations,some covariates are easily measured on all cohort subjects,and surrogate measurements of the expensive covariates also may be observed.In this paper,to make full use of the covariate data collected outside the case-cohort sample,we propose a class of weighted estimators with general time-varying weights for the additive hazards model,and the estimators are shown to be consistent and asymptotically normal.We also identify the estimator within this class that maximizes efficiency,and simulation studies show that the efficiency gains of the proposed estimator over the existing ones can be substantial in practical situations.A real example is provided.
作者机构：
[Lei, Yi-ju] Xinxiang Univ, Dept Math, Xinxiang 453000, Peoples R China.;[Qin, Hong] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Qin, Hong] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
摘要：
In this paper, we are concerned with the following problem: {(-Delta)(k)u = lambda f(x)vertical bar u vertical bar(q-2)u + g(x)vertical bar u vertical bar(k*-2)u, x is an element of Omega, u is an element of H-0(k)(Omega), where Omega is a bounded domain in R-N with N >= 2k + 1, 1 < q < 2, lambda > 0, f, g are continuous functions on Omega which are somewhere positive but which may change sign on Omega. k(*) = 2N/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.
