Now showing items 1-19 of 19

• #### A Liouville type result for fractional Schrödinger operators in 1D ﻿

(Universitat Politècnica de Catalunya, 2017-01)
Master thesis
Open Access
The aim of this master's thesis is to obtain an alternative and original proof of a Liouville type result for fractional Schrödinger operators in 1D without using a local extension problem, in the spirit of the recent work ...
• #### A negative result for hearing the shape of a triangle ﻿

(Universitat Politècnica de Catalunya, 2019-05-24)
Bachelor thesis
Open Access
Covenantee:   Princeton University
The project will consist of a mathematical research finding its place between the branches of Partial Differential Equations and Geometry, in particular dealing with inverse spectral problems of the Laplace operator. This ...
• #### Black-Scholes differential equation and its development ﻿

(Universitat Politècnica de Catalunya, 2015-07)
Bachelor thesis
Restricted access - author's decision
L'equació de Black-Scholes és una equació en derivades parcials (EDP) de tipus difusió. Aquest model introdueix que els increments de l'actiu subjacent segueixen un moviment Brownià. És un mètode eficient per calcular el ...
• #### Boundary regularity for the fractional heat equation ﻿

(Universitat Politècnica de Catalunya, 2014-09)
Bachelor thesis
Open Access
In this dissertation we present an introduction to nonlocal operators, and in particular, we study the fractional heat equation, which involves the fractional Laplacian of order 2s. In the first chapters we make a review ...
• #### 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 ...
• #### La ecuación del calor ﻿

(2014-01-31)
Other
Open Access
La ecuación del calor fue propuesta por Fourier en 1807-en su memoria sobre la propagación del calor en los cuerpos sólidos. En ella proponía además el germen de lo que pasaria a ser la Teoría de las Series de Fourier. Tan ...
• #### Elliptic and parabolic PDEs : regularity for nonlocal diffusion equations and two isoperimetric problems ﻿

(Universitat Politècnica de Catalunya, 2014-06-17)
Doctoral thesis
Open Access
The thesis is divided into two parts. The first part is mainly concerned with regularity issues for integro-differential (or nonlocal) elliptic and parabolic equations. In the same way that densities of particles with ...
• #### Estimates and rigidity for stable solutions to some nonlinear elliptic problems ﻿

(Universitat Politècnica de Catalunya, 2020-01-28)
Doctoral thesis
Open Access
Covenantee:   Università degli Studi di Milano
My thesis deals with the study of elliptic PDE. It is divided into two parts, the first one concerning a nonlinear equation involving the p-Laplacian, and the second one focused on a nonlocal problem. In the first part, ...
• #### Ground states in Mathematical Physics ﻿

(Universitat Politècnica de Catalunya, 2015-09)
Bachelor thesis
Open Access
The main aim of this bachelor's thesis is to introduce the concept of a ground state and prove its existence for the nonlinear diffusion equation $$-\Delta u + a u = b |u|^\alpha u \ \ \text{in} \ \mathbb{R}^N,$$ as well ...
• #### Integro-differential equations : regularity theory and Pohozaev identities ﻿

(Universitat Politècnica de Catalunya, 2014-06-19)
Doctoral thesis
Open Access
The main topic of the thesis is the study of Elliptic PDEs. It is divided into three parts: (I) integro-differential equations, (II) stable solutions to reaction-diffusion problems, and (III) weighted isoperimetric and ...
• #### 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 ...
• #### 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 ...
• #### Periodic solutions to PDEs with fractional diffusion ﻿

(Universitat Politècnica de Catalunya, 2016-01)
Bachelor thesis
Open Access
The aim of this Bachelor's Thesis is the study of periodic solutions to nonlinear equations involving the fractional Laplace operator. Our starting point is the Benjamin-Ono equation in water waves, a completely integrable ...
• #### Propagation in reaction-diffusion equations with fractional diffusion ﻿

(Universitat Politècnica de Catalunya, 2014-07-07)
Doctoral thesis
Open Access
Covenantee:   Université Toulouse III - Paul Sabatier
This thesis focuses on the long time behaviour of solutions to Fisher-KPP reaction-diffusion equations involving fractional diffusion. This type of equation arises, for example, in spatial propagation or spreading of ...
• #### Qualitative properties of solutions to integro-differential elliptic problems ﻿

(Universitat Politècnica de Catalunya, 2021-07-14)
Doctoral thesis
Open Access
The thesis is devoted to the analysis of elliptic PDEs and related problems. It is mainly focused on the study of qualitative and regularity properties of solutions to integro-differential equations. The study of such ...
• #### Stable and periodic solutions to nonlinear equations with fractional diffusion ﻿

(Universitat Politècnica de Catalunya, 2016-07)
Master thesis
Open Access
The aim of this thesis is to study stable solutions to nonlinear elliptic equations involving the fractional Lapacian. More precisely, we study the extremal solution for the problem $(\Delta )^s u = \lambda f(u)$ in $\Omega$, ...
• #### Stable solutions of nonlinear fractional elliptic problems ﻿

(Universitat Politècnica de Catalunya, 2019-06-18)
Doctoral thesis
Open Access
This thesis is devoted to study integro-differential equations. This type of equations constitutes nowadays a very active field of research which has important applications in modeling real-life phenomena where nonlocal ...
• #### Topics on periodic solutions to integro-differential equations ﻿

(Universitat Politècnica de Catalunya, 2020-07)
Master thesis
Open Access
This Master's Degree Thesis investigates periodic solutions to nonlinear equations involving integro-dierential operators. We show the existence and we describe these solutions for generalized Benjamin-Ono type nonlinearities, ...
• #### Uncertainty quantification for stochastic systems ﻿

(Universitat Politècnica de Catalunya, 2018-10)
Master thesis
Restricted access - author's decision
Random differential equations arise to model smooth random phenomena. The error term, instead of being introduced by means of a white noise, arises from imposing randomness to the input coefficients and initial/boundary ...