# Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error constant estimation

@article{Endo2022ShapeOF, title={Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error constant estimation}, author={Ryoki Endo and Xuefeng Liu}, journal={ArXiv}, year={2022}, volume={abs/2209.13415} }

. A computer-assisted proof is proposed for the Laplacian eigenvalue minimization problems over triangular domains under diameter constraints. The proof utilizes recently developed guaranteed computation methods for both eigenvalues and eigenfunctions of diﬀerential operators. The paper also provides an elementary and concise proof of the Hadamard shape derivative, which helps to validate the monotonicity of eigenvalue with respect to shape parameters. Beside the model homogeneous Dirichlet…

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