Now showing items 1-6 of 6

• #### 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 ...
• #### 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 ...
• #### Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties ﻿

(2014-12-01)
Article
Restricted access - publisher's policy
We investigate the equation; (-Delta(Hn))(gamma) w = f(w) in H-n,; where (-Delta(Hn))(gamma) corresponds to the fractional Laplacian on hyperbolic space for gamma is an element of(0, 1) and f is a smooth nonlinearity that ...
• #### Local integration by parts and Pohozaev indentities for higuer order fractional Laplacians ﻿

(2015-05-01)
Article
Restricted access - publisher's policy
We establish an integration by parts formula in bounded domains for the higher order fractional Laplacian (-Delta)(s) with s > 1. We also obtain the Pohozaev identity for this operator. Both identities involve local boundary ...
• #### Positive solutions of nonlinear problems involving the square root of the Laplacian ﻿

(2009-05)
External research report
Open Access
We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, ...
• #### The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary ﻿

(2014-03)
Article
Restricted access - publisher's policy
We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of (-d)su=g in O, u=0 in Rn\O, for some s¿(0, 1) and g¿L8(O), then u is Cs(Rn) ...