Document images often exhibit significant geometric distortions due to folds, curls, and non-ideal camera angles, compromising the readability and downstream text-processing performance. In this paper, we propose DocPINN, a novel single-image document dewarping framework that leverages Physics-Informed Neural Networks (PINNs) to solve a second-order partial differential equation (PDE) controlling the warp. Unlike existing methods that directly regress a dense deformation field, DocPINN infers local PDE forcing terms from image features via a convolutional network, while enforcing boundary conditions and textline constraints in a globally consistent PINN solver. This setup ensures smoother transformations in severely warped regions without sacrificing local fidelity. We conduct experiments on the DocUNet benchmark and real scanned images, demonstrating that DocPINN achieves lower character error rates (CER) and improved structural similarity (MS-SSIM) compared to state-of-the-art methods like DewarpNet. Our ablation studies confirm that the combination of learned PDE forcing, text alignment, and boundary regularization is critical for effectively resolving both large-scale perspective distortions and intricate local folds.