Let $1< q< p<\infty $, $\frac1r:=\frac1q-\frac1p $, and $ T $ be a non-degenerate Calder\'on--
Zygmund operator. We show that the commutator $[b, T] $ is compact from $ L^ p ({\mathbb …

As our main result, we supply the missing characterization of the $ L^ p (\mu)\to L^ q
(\lambda) $ boundedness of the commutator of a non-degenerate Calder\'on--Zygmund …

We study existence and regularity of solutions to the Dirichlet problem for the prescribed
Jacobian equation,\det D u= f det D u= f, where f is integrable and bounded away from zero …

We consider the class of planar maps with Jacobian prescribed to be a fixed radially
symmetric function f and which, moreover, fixes the boundary of a ball; we then study maps …

For a nonlinear operator T satisfying certain structural assumptions, our main theorem states
that the following claims are equivalent: i) T is surjective, ii) T is open at zero, and iii) T has a …

The main objects of this work are certain commutators that are applied in harmonic analysis.
Such a commutator is formed by commuting a singular integral operator and a pointwise …

Global regularity results for vectorial elliptic problems with non-quadratic growth Page 1 Global
regularity results for vectorial elliptic problems with non-quadratic growth Lukas Koch The …