$\s1$-valued Sobolev maps (2009)
We describe the structure of the space $\wsps$, where $0<\infty$ and $1\le p<\infty$. According to the values of $s$, $p$ and $n$, maps in $\wsps$ can either be characterised by their phases,...
$\s1$-valued Sobolev maps (2009)
We describe the structure of the space $\wsps$, where $0<\infty$ and $1\le p<\infty$. According to the values of $s$, $p$ and $n$, maps in $\wsps$ can either be characterised by their phases,...
An elementary proof of an inequality of Maz'ya involving $L^1$ vector fields (2009)
Bousquet, Pierre, Mironescu, Petru
We give a short elementary proof of the inequality $$\d ||D(-\Delta)^{-1}\bf{f}||_{L^{q}(|x|^{n(q-1)-q}dx)}\leq c (||\bf{f}||_{L^{1}}+||\nabla(-Delta)^{-1}\, div\, \bf{f}||_{L^{1}}), \bf{f}\in...
An elementary proof of an inequality of Maz'ya involving $L^1$ vector fields (2009)
Bousquet, Pierre, Mironescu, Petru
We give a short elementary proof of the inequality $$\d ||D(-\Delta)^{-1}\bf{f}||_{L^{q}(|x|^{n(q-1)-q}dx)}\leq c (||\bf{f}||_{L^{1}}+||\nabla(-Delta)^{-1}\, div\, \bf{f}||_{L^{1}}), \bf{f}\in...
DEGREE AND SOBOLEV SPACES (2008)
Haïm Brezis, Yanyan Li, Petru Mironescu, Louis Nirenberg
Dedicated to Jurgen Moser in friendship and admiration
On the structure of fractional degree vortices in a spinor Ginzburg-Landau model (2008)
Alama, Stan, Bronsard, Lia, Mironescu, Petru
We consider a vector--valued Ginzburg--Landau model whose minimizers exhibit vortices with half-integer degree. By studying the associated system of equations in $\RR^2$ which describes the local...
Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain (2008)
Berlyand, Leonid, Mironescu, Petru
Let $A$ be an annular type domain in $\R^2$. Let $A_\delta$ be a perforated domain obtained by punching periodic holes of size $\delta$ in $A$; here, $\delta$ is sufficiently small. Suppose that $\J$...
On the structure of fractional degree vortices in a spinor Ginzburg-Landau model (2008)
Alama, Stan, Bronsard, Lia, Mironescu, Petru
We consider a vector--valued Ginzburg--Landau model whose minimizers exhibit vortices with half-integer degree. By studying the associated system of equations in $\RR^2$ which describes the local...
Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain (2008)
Berlyand, Leonid, Mironescu, Petru
Let $A$ be an annular type domain in $\R^2$. Let $A_\delta$ be a perforated domain obtained by punching periodic holes of size $\delta$ in $A$; here, $\delta$ is sufficiently small. Suppose that $\J$...