Existence and uniqueness for double-phase Poisson equations with variable growth
Abstract
Abstract We study a class of nonlinear elliptic problems driven by a double-phase operator with variable exponents, arising in the modeling of heterogeneous materials undergoing phase transitions. The associated Poisson problem features a combination of two distinct growth conditions, modulated by a measurable weight function μ , leading to spatially varying ellipticity. Working within the framework of modular function spaces, we establish the uniform convexity of the modular associated with the gradient term. This structural property enables a purely variational treatment of the problem. As a consequence, we prove existence and uniqueness of weak solutions under natural and minimal assumptions on the variable exponents and the weight.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Navier-Stokes equation solutions
Publication details
- Journal / source
- Advances in Nonlinear Analysis
- Publisher
- Walter de Gruyter GmbH
- Volume
- 15
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN