Before revision:  As opposed to the classical DM which diverges near the boundary, the proposed GPDM estimator converges pointwise even near the boundary , assuming that the extended manifold is smooth . Applying the consistent GPDM estimator to solve the well-posed elliptic PDEs with classical boundary conditions (Dirichlet, Neumann, and Robin), we establish the convergence of the approximate solution under appropriate smoothness assumptions.
After revision:  As opposed to the classical DM which diverges near the boundary, the proposed GPDM estimator converges pointwise even near the boundary . Applying the consistent GPDM estimator to solve the well-posed elliptic PDEs with classical boundary conditions (Dirichlet, Neumann, and Robin), we establish the convergence of the approximate solution under appropriate smoothness assumptions.