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We generalise results by Lamberti and Lanza de Cristoforis (2005) concerningthe continuity of projections onto eigenspaces of self-adjoint differentialoperators with compact inverses as the (spatial) domain of the functions isperturbed in $\mathbb{R}^2$. Our main case of interest is the DirichletLaplacian. We extend these results from bounds from $H_0^1$ to $H_0^1$ tobounds from $L^p$ to $L^p$ .

$L^p$ continuity of eigenprojections for 2-d Dirichlet Laplacians under perturbations of the domain