85 research outputs found
Density in
Let be a smooth bounded domain in ,
0\textless{}s\textless{}\infty and 1\le p\textless{}\infty. We prove that
is dense in except when 1\le sp\textless{}2 and . The main
ingredient is a new approximation method for -maps when
s\textless{}1. With 0\textless{}s\textless{}1, 1\le p\textless{}\infty
and sp\textless{}n, a ball, and a general compact connected
manifold, we prove that is dense in
if and only if . This supplements
analogous results obtained by Bethuel when , and by Bousquet, Ponce and
Van Schaftingen when [General domains have been treated
by Hang and Lin when ; our approach allows to extend their result to
s\textless{}1.] The case where s\textgreater{}1, , is
still open.Comment: To appear in J. Funct. Anal. 49
Regularity of minimizers of relaxed problems for harmonic maps
AbstractWe prove that every minimizer on H1(Ω; S2) of the relaxed energy ∝¦▽u¦2 + 8πλL(u), where 0 ⩽ λ < 1 and L(u) is the length of a minimal connection connecting the singularities of u, is smooth except at a finite number of points
On some questions of topology for -valued fractional Sobolev spaces
International audienceWe describe the homotopy classes of the metric space , where is an open set in
Lifting in Sobolev spaces
International audienceWe characterize the couples with the following property: if is a complex-valued unimodular map in , then has (locally) a phase in
On a semilinear elliptic equation with inverse square potential
On a semilinear elliptic equation with inverse square potentia
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