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Tr'i Minh Le

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Preprint Sep 2026

Sharp regularity results for eikonal equations in Banach spaces

Viscosity solutions of eikonal equations need not enjoy regularity beyond Lipschitz continuity. In contrast, differentiable solutions exhibit stronger structural properties. In the Euclidean setting, building on observations of Caffarelli and Crandall (Comm. Partial Differential Equations $\textbf{35}$ (2010), 391--414...

Tr'i Minh Le, Sebastián Tapia-García · 0 citations

Preprint Jul 2026

Impossibility of a nontrivial Brunn--Minkowski inequality for higher Dirichlet eigenvalue

Let $\lambda_j(K)$ be the $j$th Dirichlet eigenvalue of a convex body $K$. It is well known that $\lambda_1$ satisfies a Brunn--Minkowski inequality: $K \mapsto \lambda_1(K)^{-1/2}$ is concave on the family of convex bodies. We show that no analogous statement holds for higher eigenvalues. More precisely, for any $j \g...

Tr'i Minh Le, Khai-Hoan Nguyen-Dang · 0 citations