A first-variation formula for eigenvalue functionals at the essential-spectrum edge characterizes all maximizing weights for Laplace and Steklov problems.
Eigenvalue optimization in higher dimensions and p-harmonic maps
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Sharp upper bounds for the first two nonzero Steklov eigenvalues on Euclidean domains in high dimensions, with strict bounds in lower dimensions and for higher eigenvalues on planar continuous-boundary domains.
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Eigenvalue optimization via a first-variation formula
A first-variation formula for eigenvalue functionals at the essential-spectrum edge characterizes all maximizing weights for Laplace and Steklov problems.
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Geometric bounds for Steklov and weighted Neumann eigenvalues on Euclidean domains
Sharp upper bounds for the first two nonzero Steklov eigenvalues on Euclidean domains in high dimensions, with strict bounds in lower dimensions and for higher eigenvalues on planar continuous-boundary domains.