一类积—微分算子的离散本征值

本文讨论的积-微分算子是一类以众多应用领域为背景的无界、非自伴线性算子.在较一般的假设下,籍助L~2空间的线性算子理论,我们证明了这类算子存在离散本征值的充分条件,并获得了可供实际工作者参考的估计式.     

Weyl Calculus for a Class of Subelliptic Operators

Weyl–Hörmander calculus is used to geta parametrix in OPS_1/2,1/2 ^1–m ()for a class of subelliptic pseudodifferential operators in OPS_1,0 ^m ()with real nonnegative principal symbol.     

The Eigenvalues of a Class of Elliptic Differential Operators

Consider $\left(M,g\right)$ as an $n$-dimensional compact Riemannian manifold. In this paper we are going to study a class of elliptic differential operators which appears naturally in the study of hypersurfaces with constant mean curvature and also the study of variation theory for $1$-area functional.     

On the Cauchy Problem for a Class of Linear Weakly Hyperbolic Operators

Abstract

We study a class of linear weakly hyperbolic operators with anisotropic degeneracy on their characteristic manifold and we give sufficient conditions for the well-posedness of the related Cauchy problem.     

一类含退化椭圆算子的Kirchhoff型方程解的存在性

利用临界点理论中的山路引理,证明一类含退化椭圆算子的Kirchhoff型方程在适当的假设条件下解的存在性,所得结论丰富和发展了已有文献的相关结果.     

Harmonic Functions for a Class of Integro-differential Operators

We consider the operator defined on functions by

一类分数阶Kirchhoff型方程非平凡解的存在性

利用临界点理论中的山路引理,研究一类分数阶Kirchhoff型方程在次临界增长条件下非平凡解的存在性,进一步统一和丰富了已有文献的相关结果.     

带势加权散度形式的 Grushin 型退化椭圆算子的 Dirichlet 特征值的上界*

本文考虑了带有位势的散度形式的 Grushin 型退化椭圆算子的 Dirichlet 加权特征值的估计.利 用傅里叶变换的方法得到了特征值的精确下界估计.然后通过试验函数的方法得到了特征值上界的杨型 不等式.     

Some Examples of Nonhypoelliptic Infinitely Degenerate Elliptic Differential Operators

This paper contains examples of nonhypoelliptic infinitely degenerate elliptic differential operators. Global nonsmooth solutions of the corresponding homogeneous equations are constructed.     

Hölder Estimates for A Class of Degenerate Elliptic Equations

In this paper we study the regularity theory of the solutions of a class of degenerate elliptic equations in divergence form. By introducing a proper distance and applying the compactness method we establish the Hölder type estimates for the weak solutions.     

L r Estimates for Degenerate Elliptic Problems

We prove L ^r estimates for the Dirichlet problem –div(a(x,u,Du))=f with f in L ^q for 1q+, where the operator satisfies (|s|)|| ^p a(x,s,), with p>1. These estimates are obtained without symmetrization and are sharp in some cases.     

Estimates of Integral Kernels for Semigroups Associated with Second-Order Elliptic Operators with Singular Coefficients

In this paper we obtain pointwise two-sided estimates for the integral kernel of the semigroup associated with second-order elliptic differential operators –(a)+b ₁+b ₂+V with real measurable (singular) coefficients, on an open set R ^N . The assumptions we impose on the lower-order terms allow for the case when the semigroup exists on L ^p () for p only from an interval in [1,), neither enjoys a standard Gaussian estimate nor is ultracontractive in the scale L ^p (). We show however that the semigroup is ultracontractive in the scale of weighted spaces L ^p (,²dx) with a suitable weight and derive an upper and lower bound on its integral kernel.     

一类粗糙核奇异积分算子的端点估计

设T_Ω是带粗糙核的Calderón-Zygmund奇异积分算子,I为任意真包含在单位圆周S~1上的闭圆弧.本文证明,若Ω支在I上并在I上单调,那么T_Ω是从Hardy空间H~1(R~2)到L~1(R~2)的有界算子当且仅当‖Ω‖_(LlogL(S~1))∞.     

带权散度型椭圆算子的低阶特征值估计

本文首先给出紧致带边(边界可以为空集)光滑度量测度空间上带权散度型算子的低阶特征值的一个一般不等式,通过使用这个一般不等式,可以得到光滑度量测度空间中有界连通区域上带权散度型算子的低阶特征值的一些万有不等式.     

加权的退化椭圆系统稳定解的Liouville定理

该文研究了加权的退化椭圆系统■其中Δ_Gu=Δ_xu+(a+1)²|x|^2aΔ_yu是Grushin算子,α,β≥0,q>1,ω(x)=(1+‖x‖⁽2(α+1)))⁽β/2(α+1)).超临界指数正稳定解的Liouville定理被建立.     

Agmon-Type Estimates for a Class of Difference Operators

We analyze a general class of self-adjoint difference operators , where V _ε is a one-well potential and ε is a small parameter. We construct a Finslerian distance d induced by H _ε and show that short integral curves are geodesics. Then we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by the Finsler distance to the well. This is analog to semiclassical Agmon estimates for Schr?dinger operators. Submitted: February 23, 2008. Accepted: May 23, 2008.     

A Class of Degenerate Elliptic Equations

Hölder continuity of solutions is proved for a new class of degenerate divergent second-order elliptic equations with weight not satisfying the Muckenhoupt condition. There is no Harnack inequality and no Sobolev embedding theorems with higher summation exponent for these equations. As an example an equation is considered in a domain divided into two parts by a hyperplane. In each part the weight function is a power one, the powers are different, and their absolute values do not exceed the space dimension.