Existence, uniqueness and regularity for elliptic p -Laplace systems with complex coefficients
Abstract
Abstract 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.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Numerical methods in inverse problems
Publication details
- Journal / source
- Advances in Calculus of Variations
- Publisher
- Walter de Gruyter GmbH
- Volume
- 19
- Issue
- 3
- Pages
- 329–351
- Publication date
- 28 April 2026
- Language
- EN