We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator
and we establish a quantitative Faber-Krahn inequality. More precisely, we show that balls …

Eigenvalue Bounds for the Fractional Laplacian: A Review Page 1 Rupert L. Frank Eigenvalue
Bounds for the Fractional Laplacian: A Review Abstract: We review some recent results on …

We consider mainly the Dirichlet realization of the Laplacian operator in Ω, when Ω is a
bounded domain in R with piecewise-C boundary (domains with corners or cracks 10.1 …

We show that on S1. 1= pd 2/Sd1. 1/the conformally invariant Sobolev inequality holds with
a remainder term that is the fourth power of the distance to the optimizers. The fourth power …

The quantitative isoperimetric inequality and related topics | Bulletin of Mathematical Sciences
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We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time
Fourier transform (STFT). To do so, we consider a deficit δ (f; Ω) which measures by how …

In a seminal work, Struwe proved that if 0≤ u∈ H˙ 1 (R n) and Γ (u):=‖ Δ u+ un+ 2 n− 2‖
H− 1→ 0, then dist (u, T)→ 0, where T denotes the manifold of sums of Aubin–Talenti …

Let Ω⊂ R d be an open set, and consider the Laplacian operator−∆ on Ω under various
boundary conditions. When the relevant spectrum happens to be discrete, it is an interesting …

We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference
between the Gaussian perimeter of a given set and a half-space with the same mass …

In this paper we study the free boundary regularity for almost-minimizers of the functional J
(u)=∫ Ω|∇ u (x)| 2+ q+ 2 (x) χ {u> 0}(x)+ q− 2 (x) χ {u< 0}(x) dx where q±∈ L∞(Ω). Almost …