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Boundary value problems for hyperholomorphic solutions of two dimensional Helmholtz equation in a fractal domain
ArticleAbstract: A theory of quaternion-valued functions, called hyperholomorphic, of two real variables has long beePalabras claves:Boundary value problems, fractal geometry, Helmholtz equations, Quaternionic analysisAutores:Reyes J.B., Ricardo Abreu Blaya, Rodríguez–Dagnino R.M.Fuentes:scopusAnalytic Riemann boundary value problem on h-summable closed curves
ArticleAbstract: The aim of this work is to further extend the notion of d-summability due to Harrison and Norton inPalabras claves:Analytic functions, Fractal dimensions, Riemann boundary value problemAutores:García T.M., Pérez Y.P., Reyes J.B., Ricardo Abreu BlayaFuentes:scopusDirichlet-Type Problems for the Two-Dimensional Helmholtz Operator in Complex Quaternionic Analysis
ArticleAbstract: This study aims to study a class of Dirichlet-type problems associated with the two-dimensional HelmPalabras claves:Dirichlet-type problems, Helmholtz operator, Quaternionic analysisAutores:Hernández-Simon L.M., Reyes J.B., Ricardo Abreu Blaya, Schneider B.Fuentes:scopusOn Riemann problems for monogenic functions in lower dimensional non-commutative Clifford algebras
ArticleAbstract: In this paper, we mainly consider the Riemann boundary value problems for lower dimensional non-commPalabras claves:Cauchy–Riemann and Dirac operators, Clifford analysis, Riemann boundary value problemAutores:Reyes J.B., Ricardo Abreu Blaya, Tamayo-Castro C.D.Fuentes:scopusOn the Laplacian vector fields theory in domains with rectifiable boundary
ArticleAbstract: Given a domain Ω in ℝ3 with rectifiable boundary, we consider main integral, and some other, theoremPalabras claves:Cauchy transform, Quaternionic analysis, Vector fields theoryAutores:Reyes J.B., Ricardo Abreu Blaya, Shapiro M.Fuentes:scopusInframonogenic functions and their applications in 3-dimensional elasticity theory
ArticleAbstract: Solutions of the sandwich equation ∂x_f∂x_=0, where ∂x_ stands for the first-order differential operPalabras claves:Clifford analysis, inframonogenic functions, Lamé system, Linear elasticityAutores:Moreno García A., Moreno García T., Reyes J.B., Ricardo Abreu BlayaFuentes:scopusJump conditions for a metaharmonic double layer potential on rectifiable closed Jordan curves in ℝ<sup>2</sup>
ArticleAbstract: This paper is concerned with jump conditions for the double layer potential associated with the two-Palabras claves:Cauchy type integral, Helmholtz equation, Layer potentials, Quaternionic analysisAutores:Reyes J.B., Ricardo Abreu BlayaFuentes:scopus∂̄ -problem for an overdetermined system with two higher dimensional variables
ArticleAbstract: Our main purpose is to describe necessary and sufficient conditions for the solvability of the ∂̄ -pPalabras claves:Clifford analysis, Conjugate harmonic functions, ∂̄-problemAutores:Reyes J.B., Ricardo Abreu BlayaFuentes:scopusThe Bochner-Martinelli transform with a continuous density: Davydov's theorem
ArticleAbstract: In this paper, we extend to the theory of functions of several complex variables, a theorem due to DPalabras claves:Bochner-Martinelli transform, Non-smooth boundaries, Sokhotski-plemelj formulaeAutores:Peña-Peña D., Reyes J.B., Ricardo Abreu BlayaFuentes:scopus