Browsing by Subject "Differential equations, Elliptic"
Now showing items 116 of 16

A facecentred finite volume method for secondorder elliptic problems
(John Wiley & sons, 20180824)
Article
Open AccessThis work proposes a novel finite volume paradigm, the facecentred finite volume (FCFV) method. Contrary to the popular vertex (VCFV) and cell (CCFV) centred finite volume methods, the novel FCFV defines the solution on ... 
A priori estimates for semistable solutions of semilinear elliptic equations
(20160201)
Article
Open AccessWe consider positive semistable solutions u of Lu + f(u) = 0 with zero Dirichlet boundary condition, where L is a uniformly elliptic operator and f is an element of C2 is a positive, nondecreasing, and convex nonlinearity ... 
An extension problem for sums of fractional Laplacians and 1D symmetry of phase transitions
(20150910)
Article
Open AccessWe study nonlinear elliptic equations for operators corresponding to nonstable Lévy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of nonstable ... 
Boundedness of stable solutions to semilinear elliptic equations: A survey
(20170501)
Article
Open AccessThis article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known L8 estimates that hold for all nonlinearities. Such estimates are ... 
Delaunay cylinders with constant nonlocal mean curvature
(Universitat Politècnica de Catalunya, 201705)
Master thesis
Open AccessThe 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 nonlocal version of the classical perimeter ... 
Diagonal cycles and Euler systems II: the Birch and SwinnertonDyer conjecture for HasseWeilArtin Lfunctions
(20170701)
Article
Open AccessThis article establishes new cases of the Birch and SwinnertonDyer conjecture in analytic rank 0, for elliptic curves over $ \mathbb{Q}$ viewed over the fields cut out by certain selfdual Artin representations of dimension ... 
From probability to PDEs : Stochastic differential equations and applications
(Universitat Politècnica de Catalunya, 201407)
Master thesis
Open AccessThe 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
(20191001)
Article
Open AccessA 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, 201701)
Bachelor thesis
Open AccessOn 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 reactiondiffusion PDEs, Sobolev inequalities, and monomial weights
(Universitat Politècnica de Catalunya, 201107)
Master thesis
Restricted access  author's decisionReactiondiffusion 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 policyNowadays 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, 201507)
Bachelor thesis
Open AccessIn recent years, there has been a surge of activity focused on the use of socalled 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, 20180330)
Article
Open AccessDomain 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 TugofWar games and the infinity Laplacian
(Universitat Politècnica de Catalunya, 201707)
Master thesis
Open AccessIn this work we introduce and analyze a new random TugofWar game in which one of the players has the power to decide at each turn whether to play a round of classical random TugofWar, or let the other player choose the ... 
Singularities for a fully nonlinear elliptic equation in conformal geometry
(201308)
External research report
Open AccessWe construct some radially symmetric solutions of the constant k equation on R n n R p , which blow up exactly at the submanifold R p R n . These are the basic models to the problem of nding complete metrics ... 
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 AccessRecientemente, 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 ...