Descomposición de Fischer y problemas de frontera para ecuaciones de Dirac de segundo orden

Abstract

In Clifford Analysis the inframonogenic functions can be seen as a noncommutative versión of the classical harmonic functions. The use of the structural sets and in the Dirac ope-rators allows us to consider a more general sandwich equation, whose solutions today are called (¿, ¿)-inframonogenic functions. In this work we obtain a new Fischer decomposi-tion for the space of homogeneous polynomials of Rm in terms of (¿, ¿)-inframonogenic functions. The obtained decomposition will be extended to a fractional context by means of the Caputo derivative and Weyl relations. In addition, some boundary value problems were studied for the inframonogenic functions, as well as for the Lame-Navier system and for ¿ higher order Dirac equations. The boundary conditions of the problems ensure their well- posedness in the Hadamard sense. In particular, it is shown that the satisfactory problema solving properties fail if orthonormal bases other than the standard one are considered.