D. Bucur

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math.AP2026

Concavity and hot spots in elliptic problems under mixed boundary conditions

Dorin Bucur, Ilaria Fragalà

We consider the torsion function and the first Laplacian eigenfunction in a convex curvilinear sector in the plane, under homogeneous Neumann conditions on the two straight lateral…

math.AP2026

Quantitative Kröger inequalities for Neumann eigenvalues of convex domains

Dorin Bucur, Andrea Gentile, Antoine Henrot

Refining the sharp upper bounds $μ_{k, d}^{*}$ obtained by Kröger (1999) for the $k$ -th Neumann eigenvalue of a convex domain $Ω \subset R^{d}$ , we prove the following inequali…

math.AP2018

Sign changing solutions of Poisson's equation

Michiel van den Berg, Dorin Bucur

Let $Ω$ be an open, possibly unbounded, set in Euclidean space $R^{m}$ with boundary $\partial Ω,$ let $A$ be a measurable subset of $Ω$ with measure $∣ A ∣$ , and let $γ \in (0, 1)$ . We…