86 citations · 208 across the 23 of their papers we have counts for
31 papers
Sharp Higher Integrability Theory, Part I: The -norm of the Beurling--Ahlfors transform
Andrea Agazzi, Kari Astala, Giuseppe Bruno +18
We confirm a conjecture posed by T. Iwaniec in 1982: the norm of the Beurling--Ahlfors transform is if , and if .
Recovering nonsmooth coefficients for higher-order perturbations of a polyharmonic operator
Russell M. Brown, Landon Gauthier, Daniel Faraco
We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator with . We show that the map from the c…
Homogenization on parallelizable Riemannian manifolds
Daniel Faraco, Luis Guijarro, Yaroslav Kurylev +1
We consider the problem of finding the homogenization limit of oscillating linear elliptic equations on an arbitrary parallelizable manifold . We replicate the concept of…
Lower semicontinuity, Stoilow factorization and principal maps
Kari Astala, Daniel Faraco, André Guerra +2
We consider a strengthening of the usual quasiconvexity condition of Morrey in two dimensions, which allows us to prove lower semicontinuity for functionals which are unbounded as…
The local Burkholder functional, quasiconvexity and Geometric Function Theory
Kari Astala, Daniel Faraco, André Guerra +2
We show that the local Burkholder functional is quasiconvex. In the limit of going to 2 we find a class of non-polyconvex functionals which are quasiconvex on th…
Magnetic helicity, weak solutions and relaxation of ideal MHD
Daniel Faraco, Sauli Lindberg, László Székelyhidi
We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics in the context of weak solutions. We introduce a relaxed…