Zobrazeno 1 - 10
of 140
pro vyhledávání: '"Verdera, J."'
Publikováno v:
Pacific J. Math. 326 (2023) 285-300
Consider a standard Cantor set in the plane of Hausdorff dimension 1. If the linear density of the associated measure $\mu$ vanishes, then the set of points where the principal value of the Cauchy singular integral of $\mu$ exists has Hausdorff dimen
Externí odkaz:
http://arxiv.org/abs/2306.05015
Publikováno v:
Analysis & PDE 16 (2023) 1621-1650
We prove the persistence of boundary smoothness of vortex patches for a non-linear transport equation in $\mathbb{R}^n$ with velocity field given by convolution of the density with an odd kernel, homogeneous of degree $-(n-1)$ and of class $C^2(\math
Externí odkaz:
http://arxiv.org/abs/2103.05356
In this paper we consider nonlocal energies defined on probability measures in the plane, given by a convolution interaction term plus a quadratic confinement. The interaction kernel is $-\log|z|+\alpha\, x^2/|z|^2, \; z=x+iy,$ with $-1 < \alpha< 1.$
Externí odkaz:
http://arxiv.org/abs/2003.13776
In this paper we characterise the minimisers of a one-parameter family of nonlocal and anisotropic energies $I_\alpha$ defined on probability measures in $\R^n$, with $n\geq 3$. The energy $I_\alpha$ consists of a purely nonlocal term of convolution
Externí odkaz:
http://arxiv.org/abs/1907.00417
Publikováno v:
In Nonlinear Analysis June 2023 231
In this paper we consider a nonlocal energy $I_\alpha$ whose kernel is obtained by adding to the Coulomb potential an anisotropic term weighted by a parameter $\alpha\in \R$. The case $\alpha=0$ corresponds to purely logarithmic interactions, minimis
Externí odkaz:
http://arxiv.org/abs/1703.07013
Publikováno v:
Anal. PDE 9 (2016) 955-1018
Given a domain D in R^d with mild geometric measure theoretic assumptions on its boundary, we show that boundedness of the principal value Riesz tranforms (witn kernel of homogeneity -(d-1)) on H\"older spaces of order alpha on the boundary of D is e
Externí odkaz:
http://arxiv.org/abs/1410.2444
In this paper we prove the sharp distortion estimates for the quasiconformal mappings in the plane, both in terms of the Riesz capacities from non linear potential theory and in terms of the Hausdorff measures.
Comment: 33 pages
Comment: 33 pages
Externí odkaz:
http://arxiv.org/abs/1002.1038
Autor:
Mattila, P., Verdera, J.
Publikováno v:
J. Eur. Math. Soc. (JEMS) 11 (2009), no. 2, 257-271
We show that L^2-bounded singular integral in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere exis
Externí odkaz:
http://arxiv.org/abs/0711.1291
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