Camilo Lelis - Academia.edu (original) (raw)

Papers by Camilo Lelis

We give a new, simpler proof of the main approximation theorem for area minimizing current contai... more We give a new, simpler proof of the main approximation theorem for area minimizing current contained in Almgren's Big regularity paper. Our proof relies on a new estimate concerning the higher integrability of the quantity called here the excess density, which in turn we link to an analogous property of harmonic multiple valued functions.

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2002

We study fine properties of currents in the framework of geometric measure theory on metric space... more We study fine properties of currents in the framework of geometric measure theory on metric spaces developed by Ambrosio and Kirchheim, and we prove a rectifiability criterion for flat currents of finite mass. We apply these tools to study the structure of the distributional Jacobians of functions in the space BnV, defined by Jerrard and Soner. We define the subspace of special functions of bounded higher variation and we prove a closure theorem.

Journal für die reine und angewandte Mathematik (Crelles Journal), 2010

In this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3-dimensiona... more In this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments. A stronger estimate was announced by Pitts and Rubistein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a famous result of Meeks, Simon and Yau on the convergence of minimizing sequences of isotopic surfaces. This result is proved in the second part of the paper.

Journal für die reine und angewandte Mathematik (Crelles Journal), 2008

In this paper we derive new simple estimates for ordinary differential equations with Sobolev coe... more In this paper we derive new simple estimates for ordinary differential equations with Sobolev coefficients. These estimates not only allow to recover some old and recent results in a simple direct way, but they also have some new interesting corollaries.

Well-Posedness for a Class of Hyperbolic Systems of Conservation Laws in Several Space Dimensions

Communications in Partial Differential Equations, 2005

Communications in Partial Differential Equations, 2007

Annali di Matematica Pura ed Applicata, 2004

Given a multiple-valued function f , we deal with the problem of selecting its single-valued bran... more Given a multiple-valued function f , we deal with the problem of selecting its single-valued branches. This problem can be stated in a rather abstract setting considering a metric space E and a finite group G of isometries of E. Given a function f , which takes values in the equivalence classes of E/G, the problem consists of finding a map g with the same domain as f and taking values in E, such that at every point t the equivalence class of g(t) coincides with f(t). If the domain of f is an interval, we show the existence of a function g with these properties which, moreover, has the same modulus of continuity of f . In the particular case where E is the product of Q copies of R n and G is the group of permutations of Q elements, it is possible to introduce a notion of differentiability for multiple-valued functions. In this case, we prove that the function g can be constructed in such a way to preserve C k,α regularity. Some related problems are also discussed.

Terceirização de tecnologia da informação (TI): um estudo de caso em uma instituição de ensino superior com base nas teorias sobre os recursos organizacionais

3. METODOLOGIA De acordo com Gil [1], essa pesquisa constitui de um estudo descritivo já que serã... more 3. METODOLOGIA De acordo com Gil [1], essa pesquisa constitui de um estudo descritivo já que serão descritas características sobre o processo de terceirização de TI, relacionando vantagens, desvantagens e os riscos envolvidos. O estudo de caso (YIN [2]) investigou a terceirização da TI em uma universidade privada do Rio Grande do Norte. O levantamento dos dados foi realizado a partir de entrevista in loco ao gestor de TI da instituição. O roteiro de entrevista era composto por oito questões que tratavam das vantagens, desvantagens, ...

Indiana University Mathematics Journal, 2006

Let n ≥ 3. We show that there is no topological vector space X ⊂ L ∞ ∩ L 1 loc (R × R n) which em... more Let n ≥ 3. We show that there is no topological vector space X ⊂ L ∞ ∩ L 1 loc (R × R n) which embeds compactly in L 1 loc , contains BV loc ∩ L ∞ and enjoys the following closure property: If f ∈ X n (R × R n) has bounded divergence and u 0 ∈ X(R n), then there exists u ∈ X(R × R n) which solves    ∂ t u + div (uf) = 0 u(0, •) = u 0 in the sense of distributions. X(R n) is defined as the set of functions u 0 ∈ L ∞ (R n) such thatũ(t, x) := u 0 (x) belongs to X(R × R n). Our proof relies on an example of N. Depauw showing an ill-posed transport equation whose vector field is "almost BV ".