Abstract
Classical linear differential equations of mathematical physics, as is known, are constructed on the basis of the important physical laws. Last time it is found, that almost all these equations can be put in Clifford Analysis and they can be obtained without application of any physical laws. This situation gives us the idea, Clifford analysis itself can suggest new generalizations of classical equations or new equations, wich may have physical contents.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Begehr H. and Gilbert R. (1978) Piecewise continuous solutions of pseudoparabolic equations in two space dimensiones, Proc. Royal Soc. Edinburgh 81 A, 153–173.
Brackx F., Delanghe R. and Sommen F. (1982) Clifford Analysis, Pitman, London.
Gürlebeck K. and Sprössig W. (1989) Quaternionic analysis and elliptic BVP, Akad. Verlag Berlin.
Goldschmidt B. (1981) Existence theorems for generalized analytic functions in Rn, Dokl. Semin. Inst. Prikl. Mat. 15, 17–23.
Habetha K. (1983) Function theory in algebras, in Complex analysis. Methods, trends and applications, Akad. Verlag Berlin, 225–237.
Hestenes D. (1982) Space-time structure of weak and electromagnetic interactions, Found. Phys. 12, 153–168.
Iftimie V. (1965) Fonctions hypercomplexes, Bull. Math. Soc. Sci. Math. R.S. Roumanie. 9(57), 279–332.
Leutwiler H. (1992) Modified Clifford analysis, Complex Variables 17, 153–171.
McIntosh A. (1989) Clifford algebras and the higher dimensional Cauchy integral, Banach Center Publ. Warsaw 22, 253–267.
Moisil Gr. C. and Teodorescu N. (1931) Fonctions holomorphes dans l’espace, Mathematica (Cluj) 5, 142–159.
Muskhelishvili N. (1953) Singular integral equations, Nordhoff, Groningen.
Obolashvili E. (1975) Three-dimensional generalized holomorphic vectors, Differ. Equations 11, 82–87.
Obolashvili E. (1988) Effective solutions of some BVP in two and three dimensional cases, in Funct. anal, methods in complex anal, and applications to PDE, Trieste, 149–172.
Obolashvili E. (1985) Some BVP for metaparabolic equations, Proc. I. Vekua Inst. Tbilisi 1, 161–164.
Obolashvili E. (1996) Some PDE in Clifford analysis Banach Center Publ. Warsaw.
Ryan J. (1995) Cauchy-Green type formulae in Clifford analysis Trans. Amer Math. Soc. 347, 1331–1341.
Vekua I. (1962) Generalized analytic functions, London, Pergamon.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Obolashvili, E. (1998). Some Partial Differential Equations in Clifford Analysis. In: Dietrich, V., Habetha, K., Jank, G. (eds) Clifford Algebras and Their Application in Mathematical Physics. Fundamental Theories of Physics, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5036-1_23
Download citation
DOI: https://doi.org/10.1007/978-94-011-5036-1_23
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6114-8
Online ISBN: 978-94-011-5036-1
eBook Packages: Springer Book Archive