Now showing items 1-20 of 78

• #### A gradient estimate for nonlocal minimal graphs ﻿

(2019-04-01)
Article
Open Access
We consider the class of measurable functions defined in all of Rn that give rise to a nonlocal minimal graph over a ball of Rn. We establish that the gradient of any such function is bounded in the interior of the ball ...
• #### A mean field equation on a torus: one-dimensional symmetry of solutions ﻿

(2003)
Article
Open Access
We study the equation $$-\Delta u=\lambda\left(\frac{e^u}{\int_\oep e^u}- \frac{1}{|\oep|}\right)\quad \text{in }\oep$$ for $u\in E$, where $E = \{ u \in H^1(\oep): u \hbox{ is doubly periodic}, \int_{\oep} u = 0 \}$ and ...
• #### A new proof of the boundedness results for stable solutions to semilinear elliptic equations ﻿

(American Institute of Mathematical Sciences, 2019-12-01)
Article
Open Access
We consider the class of stable solutions to semilinear equations -¿u=f(u) in a bounded smooth domain of Rn. Since 2010 an interior a priori L8 bound for stable solutions is known to hold in dimensions n=4 for all C1 ...
• #### A priori estimates for semistable solutions of semilinear elliptic equations ﻿

(2016-02-01)
Article
Open Access
We 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 C-2 is a positive, nondecreasing, and convex nonlinearity ...
• #### ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS ﻿

(Universitat Politècnica de Catalunya, 2017-05-30)
Exam
• #### ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS ﻿

(Universitat Politècnica de Catalunya, 2018-03-21)
Exam
• #### ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS ﻿

(Universitat Politècnica de Catalunya, 2017-04-19)
Exam
• #### ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS ﻿

(Universitat Politècnica de Catalunya, 2016-06-07)
Exam
• #### ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS ﻿

(Universitat Politècnica de Catalunya, 2018-05-29)
Exam
• #### ADVANCED COURSE IN PARTIAL DIFFERENTIAL EQUATIONS ﻿

(Universitat Politècnica de Catalunya, 2016-04-18)
Exam
• #### 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 ...
• #### Antisymmetry of solutions for some weighted elliptic problems ﻿

(2018-03-17)
Article
Open Access
This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous ...
• #### Boundedness of stable solutions to semilinear elliptic equations: A survey ﻿

(2017-05-01)
Article
Open Access
This 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 ...
• #### Curves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay ﻿

(2018-12-01)
Article
Open Access
We are concerned with hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are ...
• #### 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 ...
• #### Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian ﻿

(2010-11)
Article
Restricted access - publisher's policy
We establish sharp energy estimates for some solutions, such as global minimizers, monotone solutions and saddle-shaped solutions, of the fractional nonlinear equation 1/2 in R n. Our energy estimates hold for every ...
• #### Entire solutions of semilinear elliptic equations in R<sup>3</sup> and a conjecture of De Giorgi ﻿

(1999)
Article
Open Access
• #### EQUACIONS DE DERIVADES PARCIALS ﻿

(Universitat Politècnica de Catalunya, 2017-06-09)
Exam