Degenerate hyperbolic equations are approximated by uniformly hyperbolic ones to prove controllability in higher dimensions for the first time.
Cavalheiro, An approximation theorem for solutions of degenerate elliptic equations,Proc
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Courant's nodal domain theorem and the residual nature of simple eigenvalues under perturbations both hold for the degenerate elliptic operator A = -div(w ∇·) with w > 0 inside Ω and w = 0 on part of ∂Ω.
citing papers explorer
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Approximation of Degenerate Hyperbolic Equations with Interior Degeneracy and Applications to Controllability
Degenerate hyperbolic equations are approximated by uniformly hyperbolic ones to prove controllability in higher dimensions for the first time.
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Some Key Properties of Eigenfunctions Linked to Degenerate Elliptic Differential Operators
Courant's nodal domain theorem and the residual nature of simple eigenvalues under perturbations both hold for the degenerate elliptic operator A = -div(w ∇·) with w > 0 inside Ω and w = 0 on part of ∂Ω.