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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Optimal Lorentz estimates are established for Riesz potentials of L1 closed or co-closed forms on compact manifolds, implying bounds for the Hodge system with finite mass data.
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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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Potential Estimates and Hodge Systems with $L^1$ data on compact manifolds
Optimal Lorentz estimates are established for Riesz potentials of L1 closed or co-closed forms on compact manifolds, implying bounds for the Hodge system with finite mass data.