Tristan Bullion-Gauthier

collaborators

3 papers

math.AP2026

$L^{2}$ -regularity of minimizers of anisotropic interaction functionals

Tristan Bullion-Gauthier, Kai Xiao

We consider interaction functionals of the form \begin{equation*} ν\mapsto {\mathscr E}(ν)=\int\_{{\mathbb R}^N}\int\_{{\mathbb R}^N} W(x-y)\intdν(y)\intdν(x)+\int\_{{\mathbb R}^N}…

math.FA2026

Existence of extremal functions in higher-order affine Sobolev inequalities

Tristan Bullion-Gauthier

In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or…

math.FA2025

Higher-order affine Sobolev inequalities

Tristan Bullion-Gauthier

Zhang refined the classical Sobolev inequality $∥ f ∥_{L^{N p / (N - p)}} ≲ ∥\nabla f ∥_{L^{p}}$ , where $1 \leq p < N$ , by replacing $∥\nabla f ∥_{L^{p}}$ with a smaller quantit…

L2-regularity of minimizers of anisotropic interaction functionals

Existence of extremal functions in higher-order affine Sobolev inequalities

Higher-order affine Sobolev inequalities

$L^{2}$ -regularity of minimizers of anisotropic interaction functionals