0000000000384979
AUTHOR
Daniel Faraco
showing 8 related works from this author
Limiting Carleman weights and conformally transversally anisotropic manifolds
2020
We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, 3 3 -manifolds, and 4 4 -manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman weights, and show that there are only three basic such weights up to the action of the conformal group. In dimension three we show that if the manifold is not conformally flat, there could be one or two limiting Carleman weights. We also characterize the metrics that have more than one limiting Carleman weight. In dimension four we obtain a complete spectrum of examples according to the structure of the Weyl tensor. In particular, we construct unimodular Lie groups whose …
A short proof of the self-improving regularity of quasiregular mappings
2005
. The theoryof quasiregular mappings is a central topic in modern analysis withimportant connections to a variety of topics as elliptic partial differen-tial equations, complex dynamics, differential geometry and calculus ofvariations [13] [10].A remarkable feature of quasiregular mappings is the self-improvingregularity. In 1957 [2], Bojarski proved that for planar quasiregularmappings, there exists an exponent
Milton’s conjecture on the regularity of solutions to isotropic equations
2003
Abstract We present examples showing that the threshold for the integrability of the gradient of solutions to isotropic equations is 2K/(K−1). The main tools are p-laminates and Beltrami Operators.
Geometric rigidity of conformal matrices
2009
We provide a geometric rigidity estimate a la Friesecke-James-Muller for conformal matrices. Namely, we replace SO(n) by a arbitrary compact subset of conformal matrices, bounded away from 0 and invariant under SO(n), and rigid motions by Mobius transformations.
Manifolds of quasiconformal mappings and the nonlinear Beltrami equation
2014
In this paper we show that the homeomorphic solutions to each nonlinear Beltrami equation $\partial_{\bar{z}} f = \mathcal{H}(z, \partial_{z} f)$ generate a two-dimensional manifold of quasiconformal mappings $\mathcal{F}_{\mathcal{H}} \subset W^{1,2}_{\mathrm{loc}}(\mathbb{C})$. Moreover, we show that under regularity assumptions on $\mathcal{H}$, the manifold $\mathcal{F}_{\mathcal{H}}$ defines the structure function $\mathcal{H}$ uniquely.
Quasiregular mappings and Young measures
2002
W1,p-gradient Young measures supported in the set Q2(K) of two-dimensional K-quasiconformal matrices are studied. We prove that these Young measures can be generated by gradients of K-quasiregular mappings. This leads, for example, to the 0-1 law for quasiregular W1,p-gradient Young measures and other quasiregular properties such as higher integrability.
Improved Hölder regularity for strongly elliptic PDEs
2019
We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of H\"older regularity, higher than what is given by the classical exponent $1/K$.
Mappings of finite distortion: the degree of regularity
2005
This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)⩾1 be a measurable function defined on a domain Ω⊂Rn,n⩾2, and such that exp(βK(x))∈Lloc1(Ω), β>0. We show that there exist two universal constants c1(n),c2(n) with the following property: Let f be a mapping in Wloc1,1(Ω,Rn) with |Df(x)|n⩽K(x)J(x,f) for a.e. x∈Ω and such that the Jacobian determinant J(x,f) is locally in L1log−c1(n)βL. Then automatically J(x,f) is locally in L1logc2(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite disto…