tailieunhanh - Báo cáo hóa học: "Research Article A Boundary Value Problem for Hermitian Monogenic Functions"

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 A Boundary Value Problem for Hermitian Monogenic Functions | Hindawi Publishing Corporation Boundary Value Problems Volume 2008 Article ID 385874 7 pages doi 2008 385874 Research Article A Boundary Value Problem for Hermitian Monogenic Functions Ricardo Abreu Blaya 1 Juan Bory Reyes 2 Dixan Pena Pena 3 and Frank Sommen3 1 Facultad de Informatica y Matemdtica Universidad de Holguin Holguin 80100 Cuba 2 Departamento de Matematica Universidad de Oriente Santiago de Cuba 90500 Cuba 3 Department of Mathematical Analysis Ghent University Galglaan 2 9000 Gent Belgium Correspondence should be addressed to Dixan Pena Pena dixan@ Received 14 September 2007 Accepted 7 December 2007 Recommended by Patrick J. Rabier We study the problem of finding a Hermitian monogenic function with a given jump on a given hypersurface in Rm m 2n. Necessary and sufficient conditions for the solvability of this problem are obtained. Copyright 2008 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. 1. Introduction Hermitian Clifford analysis deals with the simultaneous null solutions of the orthogonal Dirac operators dx and its twisted counterpart dx introduced below. For a thorough treatment of this higher-dimensional function theory we refer the reader to for example 1-5 . Let ei . e2n be an orthonormal basis of the Euclidean space R2n. Consider the complex Clifford algebra C2n constructed over R2n. The noncommutative multiplication in C2n is governed by e2 -1 j 1 . 2n j ejek ekej 0 1 j k 2n. A basis for C2n is obtained by considering for a set A j1 . jk c 1 . 2n the element eA ej1 . ejk with j1 jk. For the empty set 0 we put e 1 the latter being the identity element. Any Clifford number a G C2n may thus be written as a s aAeA aA G C A 2 Boundary Value Problems and its Hermitian conjugate a is defined by ã 2 Wa eA -1 k k 1 2eA A k. A The