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Revista matemática iberoamericana, ISSN 0213-2230, 2013, Volume 29, Issue 3, pp. 1091 - 1126
The purpose of this paper is to derive some Lewy-Stampacchia estimates in some cases of interest, such as the ones driven by non-local operators. Since we will... 
Integrodifferential operators | Fractional laplacian | Variational inequalities | Physical Sciences | Mathematics | Science & Technology
Journal Article
Journal für die reine und angewandte Mathematik, ISSN 1435-5345, 01/2017, Volume 2017, Issue 729, pp. 263 - 273
We prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi [ 
Physical Sciences | Mathematics | Science & Technology
Journal Article
Annales de l'Institut Henri Poincaré. Analyse non linéaire, ISSN 0294-1449, 07/2012, Volume 29, Issue 4, pp. 479 - 500
We discuss the Γ-convergence, under the appropriate scaling, of the energy functional‖u‖Hs(Ω)2+∫ΩW(u)dx, with s∈(0,1), where ‖u‖Hs(Ω) denotes the total... 
Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 05/2012, Volume 389, Issue 2, pp. 887 - 898
The purpose of this paper is to study the existence of solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet... 
Mountain Pass Theorem | Fractional Laplacian | Integrodifferential operators | Variational techniques | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Journal of mathematical biology, ISSN 0303-6812, 1/2017, Volume 74, Issue 1, pp. 113 - 147
Journal Article
Calculus of variations and partial differential equations, ISSN 1432-0835, 08/2010, Volume 41, Issue 1-2, pp. 203 - 240
Journal Article
Nonlinear analysis, ISSN 0362-546X, 01/2014, Volume 94, pp. 156 - 170
In this paper we show the existence of non-negative solutions for a Kirchhoff type problem driven by a nonlocal integrodifferential operator, that is... 
Fractional Laplacian | Vibrating string | Kirchhoff equation | Fractional | Laplacian | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Nonlinearity
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 01/2014, Volume 101, Issue 1, pp. 1 - 26
We prove density estimates for level sets of minimizers of the energyε2s‖u‖Hs(Ω)2+∫ΩW(u)dx, with s∈(0,1), where ‖u‖Hs(Ω) denotes the total contribution from Ω... 
Variational model | Minimizers | Gagliardo norm | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Calculus of variations and partial differential equations, ISSN 1432-0835, 06/2012, Volume 48, Issue 1-2, pp. 33 - 39
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2015, Volume 367, Issue 1, pp. 67 - 102
The aim of this paper is to deal with the non-local fractional counterpart of the Laplace equation involving critical non-linearities studied in the famous... 
Mountain Pass Theorem | Best critical Sobolev constant | Critical non-linearities | Fractional Laplacian | Integrodifferential operators | Variational techniques | Physical Sciences | Mathematics | Science & Technology
Journal Article
Discrete and continuous dynamical systems, ISSN 1078-0947, 05/2013, Volume 33, Issue 5, pp. 2105 - 2137
In this paper we study the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator L-K with homogeneous Dirichlet... 
Mountain Pass Theorem | Fractional Laplacian | Integrodifferential operators | Linking Theorem | Variational techniques | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Annales de l'Institut Henri Poincaré. Analyse non linéaire, ISSN 0294-1449, 11/2017, Volume 34, Issue 6, pp. 1387 - 1428
We consider a one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We... 
Regularity theory | Free boundary problems | Nonlocal minimal surfaces | Fractional operators | Fractional harmonic replacement | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Revista matemática iberoamericana, ISSN 0213-2230, 2017, Volume 33, Issue 2, pp. 377 - 416
We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this... 
Fractional Laplacian | Neumann problem | Nonlocal operators | Physical Sciences | Mathematics | Science & Technology
Journal Article
Bulletin des sciences mathématiques, ISSN 0007-4497, 07/2012, Volume 136, Issue 5, pp. 521 - 573
This paper deals with the fractional Sobolev spaces Ws,p. We analyze the relations among some of their possible definitions and their role in the trace theory.... 
Fractional Laplacian | Nonlocal energy | Sobolev embeddings | Gagliardo norm | Fractional Sobolev spaces | Secondary | Primary | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Annali di matematica pura ed applicata, ISSN 1618-1891, 01/2012, Volume 192, Issue 4, pp. 673 - 718
... Giampiero Palatucci · Ovidiu Savin · Enrico Valdinoci Received: 17 April 2011 / Accepted: 19 December 2011 / Published online: 4 January 2012 © Fondazione Annali di... 
82B26 | 49J45 | Nonlocal energy | Gagliardo norm | 26A33 | Mathematics, general | Mathematics | Fractional Laplacian | Phase transitions | 49Q20 | Physical Sciences | Mathematics, Applied | Science & Technology
Journal Article
Mathematische annalen, ISSN 1432-1807, 10/2016, Volume 369, Issue 3-4, pp. 1283 - 1326
...: regularity, monotonicity and rigidity results Serena Dipierro 1,2 · Nicola Soave 3 · Enrico Valdinoci 1,2,4,5 Received: 26 April 2016 / Revised: 3 October 2016... 
Mathematics, general | Mathematics | Physical Sciences | Science & Technology | Infinity | Coercivity | Rigidity | Mathematics - Analysis of PDEs
Journal Article