p (x) -Stability of the Dirichlet problem for Poisson's equation with variable exponents

Key Points

• The sequence of solutions converges to the $p(x)$-Laplacian solution in a smooth domain, enhancing understanding of variable exponent behaviors.
• Key findings show that under uniform increase of $(p_j(x))$, convergence to $u_p$ occurs for fixed boundary conditions, important for mathematical models.
• This research employs techniques for the Dirichlet problem under the $p_i(x)$-Laplacian framework, providing insights into variable exponent stability.
• Results emphasize the significance of boundary conditions in convergence behaviors, suggesting further applications in mathematical physics and engineering.