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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Establishes boundedness of singular integral operators and commutators in Orlicz spaces L^Φ under Δ2 and ∇2 conditions on the Young function, providing foundation for interior regularity of higher-order elliptic operators.
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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.