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S. E. Boutiah

Publications and source records attributed to S. E. Boutiah.

5 recordsLinked to original sources
arXiv2026

Uniform many-particle spectral gap inequality and heat kernel bounds for strong attractive interactions

We prove a spectral gap inequality for Gaussian measures modified by singular attractive pair interactions. The spectral gap constant is explicit and uniform in the number of particles and the regularization parameter. As an application, we use a corresponding spectral gap inequality for a cutoff interaction weight to obtain two-sided bounds on the transition density of the attractive logarithmic gas.

math.AP↗
arXiv2026

Strong solutions of SDEs with critical discontinuities in diffusion coefficients

We prove strong existence for Itô SDEs with diffusion coefficients that can introduce strong attraction to a submanifold. We extend and strengthen the Röckner-Zhao approach, which uses Malliavin calculus to establish compactness of the approximating solutions in Wiener-Sobolev space. At least when the diffusion coefficients are sufficiently regular in time, this provides an alternative to Krylov's recent proof of strong existence via analysis of the Itô-Duhamel series.

math.PR↗
arXiv2017

Kernel estimates for elliptic operators with unbounded diffusion, drift and potential terms

In this paper we prove that the heat kernel $k$ associated to the operator $A:= (1+|x|^α)Δ+b|x|^{α-1}\frac{x}{|x|}\cdot\nabla -|x|^β$ satisfies $$ k(t,x,y) \leq c_1e^{λ_0 t+ c_2t^{-γ}}\left(\frac{1+|y|^α}{1+|x|^α}\right)^{\frac{b}{2α}} \frac{(|x||y|)^{-\frac{N-1}{2}-\frac{1}{4}(β-α)}}{1+|y|^α} e^{-\frac{\sqrt{2}}{β-α+2}\left(|x|^{\frac{β-α+2}{2}}+ |y|^{\frac{β-α+2}{2}}\right)} $$ for $t>0,\,|x|,\,|y|\ge 1$, where $b\in\mathbb{R}$, $c_1,\,c_2$ are positive constants, $λ_0$ is the largest eigenvalue of the operator $A$, and $γ=\frac{β-α+2}{β+α-2}$, in the case where $N>2,\,α>2$ and $β>α-2$. The proof is based on the relationship between the log-Sobolev inequality and the ultracontractivity of a suitable semigroup in a weighted space.

math.AP↗
arXiv2017

Elliptic operators with unbounded diffusion, drift and potential terms

We prove that the realization $A_p$ in $L^p(\mathbb{R}^N),\,1 2,\,β>α-2$ and any constants $b\in \mathbb{R}$ and $c>0$. This generalizes the recent results in [A.Canale, A. Rhandi, C. Tacelli, Ann. Sc. Norm. Super. Pisa CI. Sci. (5), 2016] and in [G.Metafune, C.Spina, C.Tacelli, Adv. Diff. Equat., 2014]. Moreover we show that $T(\cdot)$ is consistent, immediately compact and ultracontractive.

math.AP↗