Derives Clarke subdifferential and first-variation formula for the kth eigenvalue on self-adjoint operators (valid at essential spectrum edge) and applies it to characterize optimal weights in weighted Laplace/Steklov problems.
Extremal Eigenvalues of the Laplacian in a Conformal Class of Metrics: The `Conformal Spectrum' , url =
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A regularity theorem establishes that sufficiently regular stationary measures for a variational eigenvalue problem on manifolds are absolutely continuous with densities induced by harmonic maps.
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Eigenvalue optimization via a first-variation formula
Derives Clarke subdifferential and first-variation formula for the kth eigenvalue on self-adjoint operators (valid at essential spectrum edge) and applies it to characterize optimal weights in weighted Laplace/Steklov problems.
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A regularity theorem for stationary measures
A regularity theorem establishes that sufficiently regular stationary measures for a variational eigenvalue problem on manifolds are absolutely continuous with densities induced by harmonic maps.