On a generalized Lamé-Navier system in ℝ³

References

[1] Abreu Blaya, R.—Bory Reyes, J.—Guzmán, A.—Kähler, U.: On the Π-operator in Clifford analysis, J. Math. Anal. Appl. 434 (2016), 1138–1159.10.1016/j.jmaa.2015.09.038Search in Google Scholar

[2] Abreu Blaya, R.—Bory Reyes, J.—Guzmán, A.—Kähler, U.: On the ϕ-hyperderivative of the ψ-Cauchy-type integral in Clifford analysis, Comput. Methods Funct. Theory 17 (2017), 101–119.10.1007/s40315-016-0172-0Search in Google Scholar

[3] Barber, J. R.: Solid Mechanics and Its Applications, Springer, Berlin, 2003.Search in Google Scholar

[4] Brackx, F.—Delanghe, R.—Sommen, F.: Clifford Analysis, Research Notes in Mathematics 76, Pitman (Advanced Publishing Program), Boston, 1982.Search in Google Scholar

[5] Bock, S.—Gürlebeck, K.: On a spatial generatization of the Kolosov-Muskhe-lishvili formulae, Math. Methods Appl. Sci. 32 (2009), 223–240.10.1002/mma.1033Search in Google Scholar

[6] Bock, S.—Gürlebeck, K.—Legatiuk, D.—Nguyen, H. M.: ψ-Hyperholomorphic functions and a Kolosov-Muskhelishvili formula, Math. Methods Appl. Sci. 38 (2015), 5114–5123.10.1002/mma.3431Search in Google Scholar

[7] Delanghe, R.—Krausshar, R. S.—Malonek, H. R.: Differentiability of functions with values in some real associative algebras: approaches to an old problem, Bull. Soc. R. Sci. Liege. 70 (2001), 231–249.Search in Google Scholar

[8] Grigoriev, Y.: Three-dimensional quaternionic analogue of the Kolosov-Muskhelishvili formulae. In: Hypercomplex Analysis: New Perspectives and Applications, Cham: Trends Math., Birkäuser/Springer, 2014, pp. 145–166.10.1007/978-3-319-08771-9_10Search in Google Scholar

[9] Grigoriev, Y.: Regular quaternionic functions and their applications in three-dimensional elasticity, XXIV ICTAM Regular Quaternionic 21–26, Montreal, Canada, 2016.Search in Google Scholar

[10] Gürlebeck, K.: On some classes of Π-operators, in Dirac operators in analysis. In: Pitman Research Notes in Mathematics 394 (eds. J. Ryan and D. Struppa), 1998.Search in Google Scholar

[11] Gürlebeck, K.—Kähler, U.—Shapiro, M.: On the Π-operator in hyperholomorphic function theory, Adv. Appl. Clifford Algebr. 9(1) (1999), 23–40.10.1007/BF03041935Search in Google Scholar

[12] Gürlebeck, K.—Sprössig, W.: Quaternionic Analysis and Elliptic Boundary Vaule Problems, Birkhäuser AG, Basel, 1990.10.1007/978-3-0348-7295-9Search in Google Scholar

[13] Gürlebeck, K.—Nguyen, H. M.: ψ-Hyperholomorphic functions and an application to elasticity problems, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, 2014.10.1063/1.4912656Search in Google Scholar

[14] Gürlebeck, K.—Nguyen, H. M.: On ψ-hyperholomorphic functions and a decomposition of harmonics. In: Hyper Complex Analysis: New Perspectives and Applications, Trends in Mathematics, 2014, 181–189.10.1007/978-3-319-08771-9_12Search in Google Scholar

[15] Kirchhoff, G.: Vorlesungen über mathematische Physik, vol. 1, Mechanik, 4th ed., Leipzig, 1897 (1st ed. 1876) 3, I4, 48, 70, I42.Search in Google Scholar

[16] Klawitter, D.: MathWorks. Clifford Algebra; https://www.mathworks.com/matlabcentral/fileexchange/34286-clifford-algebra#feedback.Search in Google Scholar

[17] Krausshar, R. S.—Malonek, H. R.: A characterization of conformal mappings in ℝ⁴ by a formal differentiability condition, Bull. Soc. R. Sci. Liege 70(1) (2001), 35–49.Search in Google Scholar

[18] Lamé, G.: Mmoire sur les surfaces isothermes dans les corps solides homogènes en équilibre de temprature. Journal de Mathématiques Pures et Appliquées 2 (1837), 147–188.Search in Google Scholar

[19] Liu, L. W.—Hong, H. K.: Clifford algebra valued boundary integral equations for three-dimensional elasticity, Appl. Math. Modell. 54 (2018), 246–267.10.1016/j.apm.2017.09.031Search in Google Scholar

[20] Malonek, H.—Peña-Peña, D.—Sommen, F.: A Cauchy-Kowalevski theorem for inframonogenic functions, Math. J. Okayama Univ. 53 (2011), 167–172.Search in Google Scholar

[21] Malonek, H.—Peña-Peña, D.—Sommen, F.: Fischer decomposition by inframonogenic functions, CUBO 12(2) (2010), 189–197.10.4067/S0719-06462010000200012Search in Google Scholar

[22] Nguyen, H. M.: ψ-Hyperholomorphic Function Theory in ℝ³: Geometric Mapping Properties and Applications, Fakultat Bauingenieurwesen der Bauhaus-Universitat. Weimar. e-pub.uni-weimar.de, Habilitation Thesis, 2015.Search in Google Scholar

[23] Nono, K.: On the quaternion linearization of Laplacian Δ, Bull. Fukuoka Univ. Ed. III 35 (1986), 5–10.Search in Google Scholar

[24] Moreno García, A.—Moreno García, T.—Abreu Blaya, R.—Bory Reyes, J.: A Cauchy integral formula for inframonogenic functions in Clifford analysis, Adv. Appl. Clifford Algebras 27(2) (2017), 1147–1159.10.1007/s00006-016-0745-zSearch in Google Scholar

[25] Moreno García, A.—Moreno García, T.—Abreu Blaya, R.—Bory Reyes, J.: Decomposition of inframonogenic functions with applications in elasticity theory, Math. Meth. Appl. Sci. 43 (2020), 1915–1924.10.1002/mma.6015Search in Google Scholar

[26] Moreno García, A.—Moreno García, T.—Abreu Blaya, R.—Bory Reyes, J.: Inframonogenic functions and their applications in three dimensional elasticity theory, Math. Meth. Appl. Sci. 41(10) (2018), 3622–3631.10.1002/mma.4850Search in Google Scholar

[27] Niyozov, I. E.— Makhmudov, O. I.: The Cauchy problem of the moment elasticity theory in ℝ^m, Russian Mathematics (Iz. VUZ) 58(2) (2014), Art. No. 240.10.3103/S1066369X14020042Search in Google Scholar

[28] Russell, M.—Brown, I. M.: The mixed problem for the Lamé system in a class of Lipschitz domains, J. Differential Equations 246 (2009), 2577–2589.10.1016/j.jde.2009.01.008Search in Google Scholar

[29] Sadd, M. H.: Elasticity: Theory, Applications and Numerics, Elsevier, Oxford, 2005.Search in Google Scholar

[30] Shapiro, M. V.—Vasilevski, N. L.: Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems. I. ψ-hyperholomorphic function theory, Complex Variables 27 (1995), 17–46.10.1080/17476939508814803Search in Google Scholar

[31] Weisz-Patrault, D.— Bock, S.—Gürlebeck, K.: Three-dimensional elasticity based on quaternion-valued potentials, Int. J. Solids Struct. 51 (2014), 3422–3430.10.1016/j.ijsolstr.2014.06.002Search in Google Scholar