Bicomplex Schwarz and Dirichlet Boundary Value Problems
William L. Blair
TL;DR
This paper introduces and solves Schwarz and Dirichlet boundary value problems for bicomplex-valued functions on the complex unit disk, expanding classical boundary value problem theory into the bicomplex setting.
Contribution
It defines and addresses boundary value problems for bicomplex functions, a novel extension of classical complex analysis.
Findings
Established existence and uniqueness of solutions
Extended boundary value problem techniques to bicomplex functions
Provided explicit solutions for specific boundary conditions
Abstract
We define and solve boundary value problems of Schwarz and Dirichlet type on the complex unit disk for bicomplex-valued functions.
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