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The Maximal Singular Integral: Estimates in Terms of the Singular Integral [PDF]
, 2013 This is an expository paper on the characterization of the even (or odd) smooth homogeneous convolution Calderón-Zygmund operators in R^n such that the maximal singular integral can be controlled in the L^2 norm by the singular integral. We focuss attention on special cases of the general statements to convey the main ideas of the proofs in a ...
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A Regularization of Fredholm type singular integral equations
International Journal of Mathematics and Mathematical Sciences, 2001 We present a method to regularize first and second kind integral equations of Fredholm type with singular kernel. By appropriate application of the Poincaré-Bertrand formula we change such integral equations into a second kind Fredholm's integral ...
N. Aliev, S. Mohammad Hosseini
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On an Integral Equation with the Riemann Function Kernel
Axioms, 2022 This paper is concerned with a study of a special integral equation. This integral equation arises in many applied problems, including transmutation theory, inverse scattering problems, the solution of singular Sturm–Liouville and Shrödinger equations ...
Sergei Sitnik, Abdul Ahad Arian
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Approximate methods for solving degenerate singular integral equations
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2023 Background. Singular integral equations in degenerate cases describe many processes in natural science and technology. The theory of these equations has been studied quite well, but as far as the authors know, there are currently no analytical methods ...
Il'ya V. Boykov, Anastasiya A. Pivkina
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Investigation on the Singularities of Some Singular Integrals
Computer Modeling in Engineering & Sciences, 2011 In a boundary element method, the treatment of all the possible singular integrals is very important for the correctness and accuracy of the solutions. Generally, the directional derivative of a weakly singular integral is computed by an integral in the sense of Cauchy principal value if the directional derivative of the weakly singular integral kernel
Yan, Zai You, Zhang, Qiang
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Lagrangian flows for vector fields with gradient given by a singular integral [PDF]
, 2013 We prove quantitative estimates on ows of ordinary di erential equations with vector field with gradient given by a singular integral of an L1 function.
Crippa, Gianluca, Bouchut, Francois
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Computer Assisted Methods in Engineering and Science, 2017 Singular and hypersingular integral equations appear frequently in engineering problems. The approximate solution of these equations by using various numerical methods is well known.
Nikolaos I. Ioakimidis
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Multilinear singular integrals [PDF]
Publicacions Matemàtiques, 2002 We survey the thoery of multilinear singular integral operators with modulation symmetry. The basic example for this theory is the bilinear Hilbert transform and its multilinear variants. We outline a proof of boundedness of Carleson's operator which shows the close connection of this operator to multilinear singular integrals.
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, 2013 This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and
Mikhailov, SE +2 more
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Finite Element Quadrature of Regularized Discontinuous and Singular Level Set Functions in 3D Problems [PDF]
, 2012 Regularized Heaviside and Dirac delta function are used in several fields of computational physics and mechanics. Hence the issue of the quadrature of integrals of discontinuous and singular functions arises.
PONARA, Nicola +9 more
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