Existence, uniqueness and regularity for elliptic p -Laplace systems with complex coefficients

This paper concerns a class of elliptic systems of p -Laplace type with complex-valued coefficients and source terms. We extend the real-valued theory of the elliptic p -Laplace equation to the complex-valued case. We establish the existence and uniqueness of solutions to the Dirichlet problem and prove the Schauder estimate in the case of Hölder continuous coefficients and source terms. We also consider families of coefficient functions parametrized by a complex variable and prove a differentiability result for the map taking the complex parameter to the corresponding solution.