Ricardo Abreu Blaya
Other affiliations: University of Holguín
Bio: Ricardo Abreu Blaya is an academic researcher from Autonomous University of Guerrero. The author has contributed to research in topics: Clifford analysis & Boundary value problem. The author has an hindex of 13, co-authored 72 publications receiving 449 citations. Previous affiliations of Ricardo Abreu Blaya include University of Holguín.
Papers published on a yearly basis
TL;DR: In this article, the authors investigate the analogous of the Compound Riemann-Hilbert boundary value problems for quaternionic monogenic functions and establish the solution (explicitly) of the problem over continuous surface, with little smoothness, which bounds a bounded domain of R3.
Abstract: In this paper, analogous of the Compound Riemann-Hilbert boundary value problems are investigate for quaternionic monogenic functions. The solution (explicitly) of the problem is established over continuous surface, with little smoothness, which bounds a bounded domain of R3. In particular, smoothness property for high-dimensional Cauchy type integral are computed. We also use Zygmund type estimates to adapt existing one-variable complex results to ilustrate the Holder-boundedness of the singular integral operator on 2-dimensional Ahlfors regular surfaces. At the end, uniqueness of solution for the Riemann boundary value problem have already built taking as a base the general Operator Theory.
TL;DR: The main goal of as discussed by the authors is to study the behavior of the Cauchy type integral and its corresponding singular version over nonsmooth domains in Euclidean space, based on a recently developed quaternionic cauchy integrals theory within the three-dimensional setting.
Abstract: The main goal of this paper is centred around the study of the behavior of the Cauchy type integral and its corresponding singular version, both over nonsmooth domains in Euclidean space. This approach is based on a recently developed quaternionic Cauchy integrals theory [1, 5, 7] within the three-dimensional setting. The present work involves the extension of fundamental results of the already cited references showing that the Clifford singular integral operator has a proper invariant subspace of generalized Holder continuous functions defined in a surface of the (m+1)-dimensional Euclidean space.
TL;DR: In this article, the Cliffordian Cauchy transform was shown to be a continuous R 0,n-valued function on an n-dimensional rectifiable Ahlfors-David regular surface in Rn+1.
Abstract: Let Γ be an n-dimensional rectifiable Ahlfors-David regular surface in Rn+1. Let u be a continuous R0,n-valued function on Γ, where R0,n is the Clifford algebra associated with Rn. Then we prove that the Cliffordian Cauchy transform
TL;DR: In this article, boundary value problems combining Jump-Riemann and Hilbert problems for monogenic functions in Ahlfors-David regular surfaces and in the upper half space are investigated.
Abstract: In this paper boundary value problems combining Jump — Riemann and Hilbert problems for monogenic functions in Ahlfors-David regular surfaces and in the upper half space respectively are investigated. The explicit formula of the solution is obtained.
01 Jan 2016
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01 Jan 1998
01 Jan 1966
TL;DR: Boundary value problems in physics and engineering were studied in this article, where Chorlton et al. considered boundary value problems with respect to physics, engineering, and computer vision.
Abstract: Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s
TL;DR: Sokolnikoff's book as discussed by the authors differs greatly from Southwell, Timoshenko, and Love in spirit and content, and is symptomatic of the change in outlook of American mathematics over the past few decades.
Abstract: THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.