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báo cáo hóa học:" Research Article Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 513186 9 pages doi 10.1155 2010 513186 Research Article Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains Ricardo Abreu-Blaya 1 Juan Bory-Reyes 2 and Paul Bosch3 1 Departamento de Matematica Universidad de Holguin Holguin 80100 Cuba 2 Departamento de Matemdtica Universidad de Oriente Santiago de Cuba 90500 Cuba 3 Facultad de Ingenieria Universidad Diego Portales Santiago de Chile 8370179 Chile Correspondence should be addressed to Paul Bosch paul.bosch@udp.cl Received 1 December 2009 Accepted 20 March 2010 Academic Editor Gary Lieberman Copyright 2010 Ricardo Abreu-Blaya et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Monogenic extension theorem of complex Clifford algebras-valued functions over a bounded domain with fractal boundary is obtained. The paper is dealing with the class of Holder continuous functions. Applications to holomorphic functions theory of several complex variables as well as to that of the so-called biregular functions will be deduced directly from the isotonic approach. 1. Introduction It is well known that methods of Clifford analysis which is a successful generalization to higher dimension of the theory of holomorphic functions in the complex plane are a powerful tool for study boundary value problems of mathematical physics over bounded domains with sufficiently smooth boundaries see 1-3 . One of the most important parts of this development is the particular feature of the existence of a Cauchy type integral whose properties are similar to its famous complex prototype. However if domains with boundaries of highly less smoothness even nonrectifiable or fractal are allowed then customary definition of the Cauchy integral falls but the boundary value problems keep .