Analysis of Capillary Effects Modelled by Elliptic Equations with \(\varrho (x)\)-Laplacian-Like Operators and Hardy Potential

This paper investigates a class of nonlinear elliptic partial differential equations involving a \(\varrho (x)\) $\varrho (x)$ -Laplacian-like operator, inspired by capillarity phenomena. The results extend existing theory on \(\varrho (x)\) $\varrho (x)$ -Laplacian operators and contribute new insights into their application to capillarity-driven processes. This work bridges the gap between theory and applications, providing a rigorous framework for analyzing complex nonlinear systems.