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pro vyhledávání: '"Prats, Martí"'
The dimension of planar elliptic measures arising from Lipschitz matrices in Reifenberg flat domains
In this paper we show that, given a planar Reifenberg flat domain with small constant and a divergence form operator associated to a real (not necessarily symmetric) uniformly elliptic matrix with Lipschitz coefficients, the Hausdorff dimension of it
Externí odkaz:
http://arxiv.org/abs/2406.11604
Publikováno v:
In Journal de mathématiques pures et appliquées June 2024 186:205-250
Autor:
Prats, Martí
We study the stability of Triebel-Lizorkin regularity of bounded functions and Lipschitz functions under bi-Lipschitz changes of variables and the regularity of the inverse function of a Triebel-Lizorkin bi-Lipschitz map in Lipschitz domains. To obta
Externí odkaz:
http://arxiv.org/abs/2007.10070
We consider the "thin one-phase" free boundary problem, associated to minimizing a weighted Dirichlet energy of the function in $\mathbb R^{n+1}_+$ plus the area of the positivity set of that function in $\mathbb R^n$. We establish full regularity of
Externí odkaz:
http://arxiv.org/abs/1907.11604
Autor:
Prats, Martí, Tolsa, Xavier
Let $\Omega^+\subset\mathbb R^{n+1}$ be an NTA domain and let $\Omega^-= \mathbb R^{n+1}\setminus \overline{\Omega^+}$ be an NTA domain as well. Denote by $\omega^+$ and $\omega^-$ their respective harmonic measures. Assume that $\Omega^+$ is a $\del
Externí odkaz:
http://arxiv.org/abs/1904.00751
We study quasiconformal mappings in planar domains $\Omega$ and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary $\parti
Externí odkaz:
http://arxiv.org/abs/1901.07844
Autor:
Prats, Martí
In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space $F^s_{p,q}(\Omega)$ in terms of first-order differences in a uniform domain $\Omega$. The characterization is valid for any positive, non-integer real smoothnes
Externí odkaz:
http://arxiv.org/abs/1804.05780
Autor:
Faraco, Daniel, Prats, Martí
We find a complete characterization for sets of isotropic conductivities with stable recovery in the $L^2$ norm when the data of the Calder\'on Inverse Conductivity Problem is obtained in the boundary of a disk and the conductivities are constant in
Externí odkaz:
http://arxiv.org/abs/1701.06480
Autor:
Oliva, Marcos, Prats, Martí
Let $\phi$ be a quasiconformal mapping, and let $T_\phi$ be the composition operator which maps $f$ to $f\circ\phi$. Since $\phi$ may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the b
Externí odkaz:
http://arxiv.org/abs/1612.00689