In this paper, we investigate the asymptotic behavior of solutions for divergence linear elliptic equations in exterior domains with periodic coefficients. Consequently, we generalise the Liouville type result firstly established by Avellaneda and Lin.
In this note, we characterize the sharp boundary condition such that the fractional harmonic extensions with Hölder regularity up to the boundary is globally Hölder continuous. The proofs are based on estimates of fractional harmonic measure decay and uniform fractional fatness of the complement of the domain.
A unique inversion of the exponential X-ray transform of some class of symmetric 2-tensor field in a two dimensional strictly convex set is considered. The approach to inversion is based on the Cauchy problem for a Beltrami-like equation associated with $A$-analytic maps.
This article gathers notes of two lectures given at Grenoble's University in June $2023$, and is an introduction to recent works on shear layers, in collaboration with D. Bian, Y. Guo, T. Nguyen and B. Pausader.
We give a very short proof of a result proved by Cappiello-Rodino-Toft on the Weyl symbol of the inverse of the Harmonic oscillator. We also extend their results to fractional powers.
In this short note, we prove a sharp quantization for positive solutions of Lane-Emden problems in a bounded planar domain. This result has been conjectured by De Marchis, Ianni and Pacella [6, Remark 1.2].
On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
In this paper, logarithmically improved regularity criteria for the Navier--Stokes/Poisson--Nernst--Planck system are established in terms of both the pressure and the gradient of pressure in the homogeneous Besov space.
This a survey on a series of recent papers in collaboration with Emanuele Spadaro on the regularity of area-minimizing currents in codimension higher than $1$.
This paper deals with the global existence and uniqueness results for the three-dimensional incompressible Euler equations with a particular structure for initial data lying in critical spaces. In this case the BKM criterion is not known.
In this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized.
In this article we study a transport-diffusion equation in the framework of the stratified Lie groups. For this equation we will study the existence of the solutions, a maximum principle, a positivity principle and Hölder regularity.
Starting from 3D elasticity equations we derive the model of the homogenized von Kármán plate by means of $Γ$-convergence. This generalizes the recent results, where the material oscillations were assumed to be periodic.