Descomposiciones aditivas del vector de desplazamiento del sistema de Lamé-Navier
PDF

Palabras clave

Análisis de Clifford
Funciones inframonogénicas
Conjuntos estructurales
Sistema de Lamé-Navier

Cómo citar

Descomposiciones aditivas del vector de desplazamiento del sistema de Lamé-Navier. (2025). Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales. https://doi.org/10.18257/raccefyn.3101

Resumen

En el contexto del análisis de Clifford surgen las funciones inframonogénicas como las soluciones de una versión no conmutativa de la ecuación de Laplace. La aplicabilidad de estas funciones en la búsqueda de nuevas representaciones para las soluciones de la ecuación de equilibrio en Elasticidad Lineal ha sido objeto de estudio por varios investigadores. Este trabajo se centra en descomposiciones aditivas para los desplazamientos del sistema de Lamé-Navier mediante funciones inframonogénicas.

PDF

Referencias

Álvarez, L. M., García, A. M., Alejandre, M. Á., Blaya, R. A. (2023) Two Spheres Uniquely Determine Infrabimonogenic Functions. Mediterranean Journal of Mathematics, 20(318), 1-18

Barber, J., Klarbring, A. (2003) Solid mechanics and its applications. Springer, Berlin

Blaya, R. A., Reyes, J. B., Guzmán, A., Kähler, U. (2016) On the Π-operator in Clifford Analysis. Journal of Mathematical Analysis and Applications, 434, 1138-1159

Blaya, R. A., Reyes, J. B., Guzmán, A., Kähler, U. (2017) On the ϕ-Hiperderivative of the ψ-Cauchy-Type Integral in Clifford Analysis. Computational Methods and Function Theory, 17, 101-119

Bock, S., Gürlebeck, K., Legatiuk, D., Nguyen, H. M. (2015) ψ-Hyperholomorphic functions and a Kolosov-Muskhelishvili formula. Mathematical Methods in the Applied Sciences, 38, 5114-5123

Brackx, F., Delanghe, R., Sommen, F. (1982) Clifford analysis. Pitman (Advanced Publishing Program), Boston, MA, Wiley

Delanghe, R. (1970) On regular-analytic functions with values in a Clifford algebra. Mathematische Annalen, 185, 91-111

Delanghe, R. (2001) Clifford Analysis: History and Perspective. Computational Methods and Function Theory, 1(1), 107-153

Delanghe, R., Reyes, J. B. (2003) An invitation to Clifford Analysis. Ciencias Matemáticas, 21(2), 109-137

Delanghe, R., Sommen, F., Souček, V. (1992) Clifford algebra and spinor-valued functions. A function theory for the Dirac operator (Vol. 53). Nature Publishing Group

Dinh, D. C. (2014) On structure of inframonogenic functions. Advances in Applied Clifford Algebras, 31, 1-12

Fung, Y. C. (1965) Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs

García, A. M., García, T. M., Blaya, R. A., Reyes, J. B. (2017) A Cauchy integral formula for inframonogenic functions in Clifford analysis. Advances in Applied Clifford Algebras, 27, 1147-1159

García, A. M., García, T. M., Blaya, R. A., Reyes, J. B. (2018) Inframonogenic functions and their applications in three dimensional elasticity theory. Mathematical Methods in the Applied Sciences, 41, 3622-3631

García, A. M., García, T. M., Blaya, R. A., Reyes, J. B. (2020) Decomposition of inframonogenic functions with applications in elasticity theory. Mathematical Methods in the Applied Sciences, 43, 1915-1924

García, A. M., Santiesteban, D. A., Blaya, R. A. (2023) On the Dirichlet problem for second order elliptic systems in the ball. Journal of Differential Equations, 364, 498-520

Grigoriev, Y. (2016) Regular quaternionic functions and their applications in three-dimensional elasticity. XXIV ICTAM Regular Quaternionic, 1, 21-26

Gürlebeck, K., Habetha, K., Sprössig, W. (2008) Holomorphic Functions in the Plane and n-Dimensional Space. Birkhäuser Verlag, Basel

Gürlebeck, K., Nguyen, H. M. (2014) On ψ-hyperholomorphic Functions and a Decomposition of Harmonics. Hypercomplex Analysis: New Perspectives and Applications. Trends in Mathematics, 181-189

Krausshar, R., Malonek, H. (2001) A characterization of conformal mappings in IR4 by a formal differentiability condition. Bulletin de la Société Royale des Sciences de Liège, 70(1), 35-49

Lámé, G. (1837) Mémoire sur les surfaces isothermes dans les corps solides homogènes en équilibre de température. Journal de Mathématiques Pures et Appliquées, 2, 147-188

Lávicka, R. (2011) The Fischer decomposition for the H-action and its applications. Hypercomplex analysis and applications trends in mathematics. Edited by Sabadini and F. Sommen, 1

Malonek, H., Peña-Peña, D., Sommen, F. (2010) Fischer decomposition by inframonogenic functions. CUBO A Mathematical Journal, 12, 189-197

Malonek, H., Peña-Peña, D., Sommen, F. (2011) A Cauchy-Kowalevski Theorem for Inframonogenic Functions. Math. J. Okayama Univ., 53, 167-172

Malvern, L. (1969) Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Upper Saddle River, NJ

Marsden, J., Hughes, T. (1983) Mathematical foundations of elasticity. Dover Publications

Muskhelishvili, N. (1953) Some basic problems of the mathematical theory of elasticity (Vol. 15). Noordhoff Groningen, Springer

Nguyen, H. M. (2015) ψ-Hyperholomorphic Function Theory in R3: Geometric Mapping Properties and Applications [Tesis doctoral, Fakultät Bauingenieurwesen der Bauhaus-Universität]

Nôno, K. (1986) On the quaternion linearization of Laplacian ∆. Bulletin of Fukuoka University of Education. Part III. Mathematics, Natural Sciences and Technology, 35, 5-10

Nôno, K., Inenaga, Y. (1987) On the Clifford linearization of Laplacian. Journal of the Indian Institute of Science, 67(5-6), 203-208

Patrault, D. W., Bock, S., Gürlebeck, K. (2014) Three-dimensional elasticity based on quaternionvalued potentials. International Journal of Solids and Structures, 51, 3422-3430

Peña, C. Á., Morais, J., Porter, R. M. (2023) Reduced-quaternion inframonogenic functions on the ball. Mathematical Methods in the Applied Sciences, 46(18), 18935-18951

Reséndis, F., Shapiro, M. (2002) Recent advances in hypercomplex analysis. Carta Informativa, Sociedad Matemática Mexicana, Marzo, 11-14

Reyes, J. B., Schepper, H. D., Adán, A. G., Sommen, F. (2016) Higher order Borel-Pompeiu representations in Clifford analysis. Mathematical Methods in the Applied Sciences, 39, 4787-4796

Ricardo, J. L. S., Blaya, R. A., Reyes, J. B., Ortiz, J. S. (2022) On a Riemann–Hilbert boundary value problem for (ϕ,ψ)-harmonic functions in Rm. Georgian Mathematical Journal, 29, 445-454

Russell, M., Brown, I. (2009) The mixed problem for the Lamé system in a class of Lipschitz domains. Journal of Differential Equations, 246, 2577-2589

Ryan, J. (2000) Basic Clifford analysis. Cubo Matemática Educacional, 2, 226-256

Ryan, J. (2004) Introductory Clifford Analysis. En Ablamowicz, R. y Sobczyk, G. (Eds.) Lectures on Clifford (geometric) algebras and applications. Birkhäuser, Boston, MA

Sadd, M. (2005) Elasticity: Theory, Applications and Numerics. Elsevier, Oxford

Santiesteban, D. A. (2024) ∂-problem for a second order elliptic system in Clifford analysis. Mathematical Methods in the Applied Sciences, 47, 9718-9728

Santiesteban, D. A., Blaya, R. A. (2022) Isomorphisms of partial differential equations in Clifford analysis. Advances in Applied Clifford Algebras, 32(10), 1-18

Santiesteban, D. A., Blaya, R. A., Alejandre, M. Á. (2022a) On (φ,ψ)-inframonogenic functions in Clifford analysis. Bulletin of the Brazilian Mathematical Society, New Series, 53, 605-621

Santiesteban, D. A., Blaya, R. A., Alejandre, M. Á. (2022b) On a generalized Lamé-Navier system in R3. Mathematica Slovaca, 72(6), 1527-1540

Santiesteban, D. A., Blaya, R. A., Alejandre, M. Á. (2023) Buscando estructuras en las soluciones de un sistema generalizado de Lamé-Navier. Publicaciones e Investigación, 17(1), 1-9

Santiesteban, D. A., Blaya, R. A., Pérez, Y. P., Almira, J. S. (2024) Fractional Fischer decompositions by inframonogenic functions. Journal of Mathematical Analysis and Applications, 539, 128468

Santiesteban, D. A., Blaya, R. A., Reyes, J. B. (2023) Boundary value problems for a second-order elliptic partial differential equation system in Euclidean space. Mathematical Methods in the Applied Sciences, 46, 15784-15798

Santiesteban, D. A., Pérez, Y. P., Blaya, R. A. (2022) Generalizations of harmonic functions in Rm. Analysis and Mathematical Physics, 12(10), 1-12

Shapiro, M. V., Vasilevski, N. (1995) Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems. I. ψ-hyperholomorphic function theory. Complex Variables, 27, 17-46

Shapiro, M. (1997) On the conjugate harmonic functions of M. Riesz-E. Stein-G. Weiss. En Dimiev, S. et al. (Eds.), Topics in Complex Analysis, Differential Geometry and Mathematical Physics. Third International Workshop on Complex Structures and Vector Fields, St. Konstantin, Bulgaria, Agosto, 23-29

Sommen, F., Sprössig, W. (2002) Introduction to Clifford analysis. Mathematical Methods in the Applied Sciences, 25(6), 1337-1342

Valencia, D. G., Blaya, R. A., Alejandre, M. Á. (2021) On the Plane Lamé-Navier System in Fractal Domains. Complex Analysis and Operator Theory, 15, 1-15

Valencia, D. G., Blaya, R. A., Alejandre, M. Á., Pérez, Y. P. (2023) On the Riemann problem in fractal elastic media. Analysis and Mathematical Physics, 13(1), 1-15

Wang, L., Jia, S., Luo, L., Qiu, F. (2022) Plemelj formula of inframonogenic functions and their boundary value problems. Complex Variables and Elliptic Equations, 68(7), 1158-1181

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.

Derechos de autor 2024 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales