Now showing items 1-18 of 18

• #### A face-centred finite volume method for second-order elliptic problems ﻿

(John Wiley & sons, 2018-08-24)
Article
Open Access
This work proposes a novel finite volume paradigm, the face-centred finite volume (FCFV) method. Contrary to the popular vertex (VCFV) and cell (CCFV) centred finite volume methods, the novel FCFV defines the solution on ...
• #### An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions ﻿

(2015-09-10)
Article
Open Access
We study nonlinear elliptic equations for operators corresponding to non-stable Lévy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of non-stable ...
• #### Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations ﻿

(2014)
External research report
Open Access
In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences ...
• #### Delaunay cylinders with constant non-local mean curvature ﻿

(Universitat Politècnica de Catalunya, 2017-05)
Master thesis
Open Access
The aim of this master's thesis is to obtain an alternative proof, using variational techniques, of an existence result for periodic sets in $\mathbb{R}^2$ that minimize a non-local version of the classical perimeter ...
• #### Delaunay hypersurfaces with constant nonlocal mean curvature ﻿

(2017-08-12)
Article
Restricted access - publisher's policy
We study hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated with critical points of the fractional perimeter functional under a volume constraint. We establish the ...
• #### Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions ﻿

(2017-07-01)
Article
Open Access
This article establishes new cases of the Birch and Swinnerton-Dyer conjecture in analytic rank 0, for elliptic curves over $\mathbb{Q}$ viewed over the fields cut out by certain self-dual Artin representations of dimension ...
• #### From probability to PDEs : Stochastic differential equations and applications ﻿

(Universitat Politècnica de Catalunya, 2014-07)
Master thesis
Open Access
The goal of this project is to give probabilistic representations of solution of different types of PDEs. In particular, we study the Brownian motion and relate this concept with the solution of linear PDEs. Moreover, we ...
• #### Improving bounds on the order of regular graphs of girth 5 ﻿

(2019-10-01)
Article
Open Access
A -graph is a -regular graph with girth and a -cage is a -graph with the fewest possible number of vertices . Constructing -cages and determining the order are both very hard problems. For this reason, an intensive line ...
• #### Layer potentials in boundary value problems and aerodynamics ﻿

(Universitat Politècnica de Catalunya, 2017-01)
Bachelor thesis
Open Access
On this Bachelor's Thesis we apply the method of layer potentials on two different contexts. On the first part of this work we will prove some important properties of the single and double layer potentials for the Laplacian ...
• #### Minimizers to reaction-diffusion PDEs, Sobolev inequalities, and monomial weights ﻿

(Universitat Politècnica de Catalunya, 2011-07)
Master thesis
Restricted access - author's decision
Reaction-diffusion equations play a central role in PDE theory and its applications to other sciences. They also play an important role in geometric problems: the problem of prescribing a curvature on a manifold and parabolic ...
• #### Orders of CM elliptic curves modulo p with at most two primes ﻿

(2010)
Article
Restricted access - publisher's policy
Nowadays the generation of cryptosystems requires two main aspects. First the security, and then the size of the keys involved in the construction and comunication process. About the former one needs a di±cult ...
• #### PDEs with fractional diffusion ﻿

(Universitat Politècnica de Catalunya, 2015-07)
Bachelor thesis
Open Access
In recent years, there has been a surge of activity focused on the use of so-called fractional diffusion operators to replace the standard Laplace operator, with the aim of further extending the theory by taking into account ...
• #### Proper generalized decomposition solutions within a domain decomposition strategy ﻿

(John Wiley & sons, 2018-03-30)
Article
Open Access
Domain Decomposition strategies and the Proper Generalized Decomposition are efficiently combined to obtain a fast evaluation of the solution approximation in parameterized elliptic problems with complex geometries. The ...
• #### Random Tug-of-War games and the infinity Laplacian ﻿

(Universitat Politècnica de Catalunya, 2017-07)
Master thesis
Open Access
In this work we introduce and analyze a new random Tug-of-War game in which one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the ...
• #### Regularity of radial stable solutions to semilinear elliptic equations for the fractional laplacian ﻿

(2018-11-01)
Article
Open Access
• #### Sobolev and isoperimetric inequalities with monomial weights ﻿

(2013)
Article
Restricted access - publisher's policy
We consider the monomial weight |x1|A1⋯|xn|An in Rn, where Ai⩾0 is a real number for each i=1,…,n, and establish Sobolev, isoperimetric, Morrey, and Trudinger inequalities involving this weight. They are the analogue of ...
• #### Solución de ecuaciones diferenciales elípticas en regiones planas irregulares usando mallas convexas generadas por métodos variacionales empleando elementos finitos ﻿

(Universitat Politècnica de Catalunya. CIMNE, 2010)
Article
Open Access
Recientemente, con el objeto de ser usadas para aproximar la solución de ecuaciones diferenciales parciales en dominios de forma irregular empleando diferencias finitas, se han propuesto varios métodos variacionales ...
• #### Some constructions for the fractional Laplacian on noncompact manifolds ﻿

(2015-01-01)
Article
Open Access
We give a definition of the fractional Laplacian on some noncompact manifolds, through an extension problem introduced by Caffarelli-Silvestre. While this definition in the compact case is straightforward, in the noncompact ...