Solución para ecuaciones elípticas de segundo orden no homogéneas en álgebras de tipo Clifford
Resumen
En el presente trabajo, nosotros usamos álgebras de Clifford generalizadas llamadas álgebras de tipo Clifford o álgebras dependiendo de parámetros, para obtener soluciones distribucionales de la ecuación Δ̃ =ℎ, donde h es una función integrable y Δ̃ es conocido como el Laplaciano en el álgebra paramétrica o simplemente Laplaciano generalizado. Para hacer esto, nosotros usamos el Kernel de Newton paramétrico.
Palabras clave: Soluciones distribucionales, Operadores elípticos, Álgebras de tipo Clifford, Formulas de Representación integral
Citas
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H. Begehr, Integral representations in complex, hypercomplex and Clifford analysis. Integral transform and Special Functions 13, 223-241, (2002)
H. Begehr, R. Gilbert, Wen-Chung Guo. Partial Differential and Integral Equations (International Society for Analysis, Aplications and Computation, International Society for Analysis, Applications and Computation. Book 2). Springer; Softcover reprint of the original (1999) edition
B-Y Yang and N. Nagaosa Classification of stable three-dimensional Dirac semimetals with nontrival topology. Nature Communications 5,4898, (2014)
E. Ariza, A. Di Teodoro A, A. Infante, and J. Vanegas, Fundamental Solutions for Second Order Elliptic Operators in Clifford-Tpe Algebras. Adv. Appl. Clifford-Type Alegrad. Adv. Appl. Clifford Algebras 25,527-538, (2015)
C. Balderrama, A. DiTeodoro A, and A. Infante, Some integral representation for metamonogenic funtions in Clifford algebras depending on parameters. Adv. Appl. Clifford Algebras 23,793-813, (2013)
M. Balk. Polyanalytic functions, Berlin: Akademie Verlag, (1991
H. Begehr, Boundary value problems in complex analysis I and II. Boletin de la Asociación de Matemática Venezolana, Vol. XII, Nro 1-2, 65-85, 217-250, (2005)
H. Begehr, Integral representations in complex, hypercomplex and Clifford analysis. Integral transform and Special Functions 13, 223-241, (2002)
H. Begehr, R. Gilbert, Wen-Chung Guo. Partial Differential and Integral Equations (International Society for Analysis, Aplications and Computation, International Society for Analysis, Applications and Computation. Book 2). Springer; Softcover reprint of the original (1999) edition
