Evaluation of strongly singular domain integrals for internal stresses in functionally graded materials analyses using RIBEM

An accurate evaluation of strongly singular domain integral appearing in the stress representation formula is a crucial problem in the stress analysis of functionally graded materials using boundary element method.To solve this problem,a singularity separation technique is presented in the paper to split the singular integral into regular and singular parts by subtracting and adding a singular term.The singular domain integral is transformed into a boundary integral using the radial integration method.Analytical expressions of the radial integrals are obtained for two commonly used shear moduli varying with spatial coordinates.The regular domain integral,after expressing the displacements in terms of the radial basis functions,is also transformed to the boundary using the radial integration method.Finally,a boundary element method without internal cells is established for computing the stresses at internal nodes of the functionally graded materials with varying shear modulus.

THE SOLUTION OF INTEGRAL EQUATIONS WITH STRONGLY SINGULAR KERNELS APPLIED TO THE TORSION OF CRACKED CIRCULAR CYLINDER

In this paper, the functions of warping displacement interruption defined on the crack lines are taken for the fundamental unknown functions. The torsion problem of cracked circular cylinder is reduced to solving a system of integral equations with strongly singular kernels. Using the numerical method of these equations, the torsional rigidities and the stress intensity factors are calculated to solve the torsion problem of circular cylinder with star-type and other different types of cracks. The numerical results are satisfactory.

Weighted estimates for strongly singular integral operators with rough kernels

The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.

Oscillatory Strongly Singular Integral Associated to the Convex Surfaces of Revolution

Here we consider the following strongly singular integral TΩ,γ,α,βf（x,t）=∫R^ne^i｜y｜^-βΩ（y/｜y｜）/｜y｜^n＋af（x-y,t-γ（｜y｜））dy, where Ω∈L^p（S^n-1）,p〉1,n〉1,α〉0 and γis convex on （0,∞）.We prove that there exists A（p,n） 〉 0 such that if β 〉 A（p,n） （1 ＋α）, then TΩ,γ,α,β is bounded from L^2 （R^n＋1） to itself and the constant is independent of γ Furthermore,when Ω∈ C^∞ （S^n-1 ）, we will show that TΩ,γ,α,β is bounded from L^2 （R^n＋l） to itself only if β〉 2α and the constant is independent of γ.

Toeplitz operators related to strongly singular Calderón-Zygmund operators

In this paper, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and Lipschitz function b∈Λβ0(Rn) is discussed from Lp(Rn) to Lq(Rn), 1/q=1/p-β0/n, and from Lp(Rn) to Triebel-Lizorkin space Fβ0,∞p. We also obtain the boundedness of generalized Toeplitz operatorθbα0 from LP(Rn) to Lq(Rn), 1/q =1/p-α0+β0/n. All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and BMO function b is discussed on LP(Rn), 1 < p <∞.

Strongly Singular Calderón-Zygmund Operator and Commutator on Morrey Type Spaces

In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space. Moreover, the boundedness of strongly singular Calderón- Zygmund operator on the predual of Morrey space is discussed.

Strongly Singular Integral Operators on Weighted Hardy Space

In this paper, we obtain that a strongly singular integral operator is bounded on Lω^p. space for 1 〈 p 〈 ∞. We also obtain that a strongly singular integral operator is a bounded operator from Hω^p, to Lω^p for some weight w and 0 〈 p ≤ 1. And by an atomic decomposition, we obtain that a strongly singular integral operator is a bounded operator on Hω^p for some w and 0 〈 p ≤ 1.

Weighted Estimates for Commutators of Strongly Singular Calderón–Zygmund Operators

In this paper, the authors establish the boundedness of commutators generated by strongly singular CalderSn-Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding results for commutators generated by strongly singular CalderSn- Zygmund operators and weighted Lipschitz functions can also be obtained.

The Commutators of Strongly Singular Integral Operators on the Weighted Hardy Spaces

Let T be a strongly singular Calderon-Zygmund operator and b∈L_(loc)(R^(n)).This article finds out a class of non-trivial subspaces BMO_(ω,p,u)(R^(n))of BMO(R^(n))for certain ω∈A_(1),0<p≤1 and 1<u≤∞,such that the commutator[b,T]is bounded from weighted Hardy space H_(ω)^(p)(R^(n))to weighted Lebesgue space L_(ω)^(p)(R^(n))if b∈BMO_(ω,p,∞)(R^(n)),and is bounded from weighted Hardy space H_(ω)^(p)(R^(n)) to itself if T^(∗)1=0 and b∈BMO_(ω,p,u)(R^(n))for 1<u<2.

Strongly Singular Convo1ution Operators on the Weighted Herz-Type Hardy Spaces

Let 0【p≤1q【0, and w1, w2 ∈A1 （Muckenhoupt-class）. In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HKqα,p（w1; w2） to the homogeneous weighted Herz spaces Kqα,p（w1;w2）, provided α=n（1--1/q）. Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HKqα,p（w1, w2） is also investigated.

Weakly Strongly Singular Integral Operators on Anisotropic Hardy Spaces and Their Dual Operators

Let A be an expansive dilation. We define weakly strongly singular integral kernels and study the action of the operators induced by these kernels on anisotropic Hardy spaces associated with A.

INTERACTION OF STRONG AND WEAK SINGULARITIES FOR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN MULTIDIMENSIONAL SPACE

In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.

Existence of Positive Solutions for the Nonhomogeneous Schrodinger-Poisson System with Strong Singularity

In this paper,a class of nonhomogeneous Schrodinger-Poisson systems with strong singularity are considered.Combining with the variational method and Nehari method,we obtain a positive solution for this system which improves the recent results in the literature.