Solutions of boundary value problems by fixed point methods in clifford analysis

Abstract:

Boundary value problems for elliptic equations of type Lu = F in higher dimensions, can be reduced to fixed-point problems for a suitable defined operator. This defined operator involves a fundamental solution of the equation Lu = 0. We consider the case when the right-hand side depends also on the function u itself and on its derivatives ∂j u for j = 1, . . ., n. As L, we consider operators in the framework of Clifford analysis as the generalized Cauchy-Riemann operator in Rn+1 . To solve the equivalent fixed-point problem, we apply the Contraction Mapping Principle and Schauder type estimates.

Año de publicación:

2021

Keywords:

• Fixed-point Theorems
• Clifford algebras
• Fundamental solutions
• Boundary value problems

Fuente:

scopus