{"ID":2921825,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-03T05:56:00.181519634Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.01383","arxiv_id":"2606.01383","title":"A symmetry formula for the spectral fractional Laplacian, and applications to boundary controllability for plate equation with structural damping","abstract":"Let $Δ$ be the Dirichlet Laplacian on a bounded domain $Ω\\subset \\mathbb{R}^{N}$, and let $(-Δ)^α$ be the associated spectral fractional Laplacian with $α\\leq 1, \\ ρ\u003c2$. For general bounded domains with $C^2$ boundary, we prove a symmetry formula for $α\u003c1/2$, extending a result previously proven on rectangles for $α\u003c1$. As a consequence of this formula, well-posedness results are proven for the structurally damped plate equation $$u_{tt}+Δ^2u+(-Δ)^αu_t=0$$ subject to Dirichlet or moment boundary control. For rectangular domains with $α\u003c1$, we prove boundary null-controllability results. For $α\u003c1/2, \\ ρ\\leq 2$, Dirichlet null controllability is proved for the unit disk in $\\mathbb{R}^2$. This analysis then extended to the classical case, $α=1$, on rectangles, where higher regularity is required for Dirichlet control.","short_abstract":"Let $Δ$ be the Dirichlet Laplacian on a bounded domain $Ω\\subset \\mathbb{R}^{N}$, and let $(-Δ)^α$ be the associated spectral fractional Laplacian with $α\\leq 1, \\ ρ\u003c2$. For general bounded domains with $C^2$ boundary, we prove a symmetry formula for $α\u003c1/2$, extending a result previously proven on rectangles for $α\u003c1$...","url_abs":"https://arxiv.org/abs/2606.01383","url_pdf":"https://arxiv.org/pdf/2606.01383v1","authors":"[\"Sergei Avdonin\",\"Julian Edward\"]","published":"2026-05-31T18:11:54Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}