3 papers
math.AP2021
Some remarks on a formula for Sobolev norms due to Brezis, Van Schaftingen and Yung
Arkady Poliakovsky
We provide answers to some questions raised in a recent work by H. Brezis, J. Van Schaftingen and Po-Lam Yung concerning the Gagliardo semi-norm computed at …
math.AP2020
On a variational approach to the Navier-Stokes Equations
Arkady Poliakovsky
Weak solutions of incompressible Navier-Stokes Equations re-obtained variationally
math.AP2018
Asymptotic behavior of the -norm of mollified functions and applications to singular perturbation problems
Arkady Poliakovsky
Motivated by results of Figalli and Jerison and Hernández, we prove the following formula: \begin{equation*} \lim_{ε\to 0^+}\frac{1}{|\lnε|}\big\|η_ε*u\big\|^q_{W^{1/q,q}(Ω)}= C_0\…