Zobrazeno 1 - 10
of 321
pro vyhledávání: '"De Lellis, Camillo"'
Autor:
De Lellis, Camillo
The aim of the note is to illustrate some of the ideas introduced by Luis Caffarelli in his groundbreaking works on the regularity theory for elliptic free boundary problems, in a way which can be understood by non-experts.
Externí odkaz:
http://arxiv.org/abs/2408.07007
We consider the following classical conjecture of Besicovitch: a $1$-dimensional Borel set in the plane with finite Hausdorff $1$-dimensional measure $\mathcal{H}^1$ which has lower density strictly larger than $\frac{1}{2}$ almost everywhere must be
Externí odkaz:
http://arxiv.org/abs/2404.17536
We study fine structural properties related to the interior regularity of $m$-dimensional area minimizing currents mod$(q)$ in arbitrary codimension. We show: (i) the set of points where at least one tangent cone is translation invariant along $m-1$
Externí odkaz:
http://arxiv.org/abs/2403.15889
Autor:
De Lellis, Camillo, Focardi, Matteo
The aim of these notes is to give a complete self-contained account of the current state of the art in the regularity for planar minimizers and critical points of the Mumford-Shah functional.
Externí odkaz:
http://arxiv.org/abs/2308.14660
We consider codimension $1$ area-minimizing $m$-dimensional currents $T$ mod an even integer $p=2Q$ in a $C^2$ Riemannian submanifold $\Sigma$ of the Euclidean space. We prove a suitable excess-decay estimate towards the unique tangent cone at every
Externí odkaz:
http://arxiv.org/abs/2308.08704
Autor:
De Lellis, Camillo, Fleschler, Ian
We generalize a classical theorem of Besicovitch, showing that, for any positive integers $k
Externí odkaz:
http://arxiv.org/abs/2307.02866
Autor:
Bressan, Alberto, De Lellis, Camillo
Given a strictly hyperbolic $n\times n$ system of conservation laws, it is well known that there exists a unique Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation, which are limits of vanishing viscosi
Externí odkaz:
http://arxiv.org/abs/2305.17203
We consider an area-minimizing integral current $T$ of codimension higher than $1$ in a smooth Riemannian manifold $\Sigma$. In a previous paper we have subdivided the set of interior singular points with at least one flat tangent cone according to a
Externí odkaz:
http://arxiv.org/abs/2304.11555
We consider an area-minimizing integral current of dimension $m$ and codimension at least $2$ and fix an arbitrary interior singular point $q$ where at least one tangent cone is flat. For any vanishing sequence of scales around $q$ along which the re
Externí odkaz:
http://arxiv.org/abs/2304.11552
We consider an area-minimizing integral current $T$ of codimension higher than 1 ins a smooth Riemannian manifold $\Sigma$. We prove that $T$ has a unique tangent cone, which is a superposition of planes, at $\mathcal{H}^{m-2}$-a.e. point in its supp
Externí odkaz:
http://arxiv.org/abs/2304.11553