Physics-Informed Neural Networks for Eigenvalue Approximation in p-Laplacian Equation with Nonhomogeneous Robin Boundary Conditions

Source abstract

This work focuses on the p-Laplacian eigenvalue problem under Robin boundary conditions. We prove results on the existence and uniqueness of its solutions, and we employ Physics-Informed Neural Networks (PINNs) to approximate the first eigenvalue. The convergence of the method is established with suitable conditions. To validate the approach, we compare the obtained approximations with exact solutions on several test problems.