2018, Lecture Notes in Mathematics, ISBN 9783319740416, Volume 2211, 224

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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

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

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

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

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

... in competition?
Annalisa Massaccesi 1 · Enrico Valdinoci 2
Received: 11 March 2015 / Revised: 28 March 2016 / Published online: 7 May 2016
© Springer-Verlag Berlin...

46N60 | Fractional equations | Mathematical and Computational Biology | Mathematics | Population dynamics | Applications of Mathematics | 35Q92 | Biology | Life Sciences & Biomedicine - Other Topics | Life Sciences & Biomedicine | Science & Technology | Mathematical & Computational Biology | Environment | Animal Distribution | Animals | Models, Biological | Ecosystem | Population Dynamics | Competition (Biology) | Usage | Analysis | Population biology | Laplacian operator | Index Medicus

46N60 | Fractional equations | Mathematical and Computational Biology | Mathematics | Population dynamics | Applications of Mathematics | 35Q92 | Biology | Life Sciences & Biomedicine - Other Topics | Life Sciences & Biomedicine | Science & Technology | Mathematical & Computational Biology | Environment | Animal Distribution | Animals | Models, Biological | Ecosystem | Population Dynamics | Competition (Biology) | Usage | Analysis | Population biology | Laplacian operator | Index Medicus

Journal Article

Calculus of variations and partial differential equations, ISSN 1432-0835, 08/2010, Volume 41, Issue 1-2, pp. 203 - 240

... Caffarelli · Enrico Valdinoci
Received: 19 November 2009 / Accepted: 18 July 2010 / Published online: 12 August 2010
© Springer-Verlag 2010
Abstract We consider nonlocal...

53A10 | 28A75 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 49Q05 | 49Q15 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Boundary conditions | Calculus of variations | Estimating techniques | Lower bounds | Minimal surfaces | Mathematical analysis | Cleaning | Density | Estimates | Optimization | Constraining

53A10 | 28A75 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 49Q05 | 49Q15 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Boundary conditions | Calculus of variations | Estimating techniques | Lower bounds | Minimal surfaces | Mathematical analysis | Cleaning | Density | Estimates | Optimization | Constraining

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

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

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

...Calc. Var. (2013) 48:33–39
DOI 10.1007/s00526-012-0539-7 Calculus of Variations
Regularity of nonlocal minimal cones in dimension 2
Ovidiu Savin · Enrico...

28A75 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 26A33 | 49Q15 | 35B65 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Cones | Minimal surfaces | Partial differential equations | Mathematical analysis | Regularity | Calculus of variations

28A75 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 26A33 | 49Q15 | 35B65 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Cones | Minimal surfaces | Partial differential equations | Mathematical analysis | Regularity | Calculus of variations

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

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

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

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

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

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

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

Mathematics, general | Mathematics | Physical Sciences | Science & Technology | Infinity | Coercivity | Rigidity | Mathematics - Analysis of PDEs

Journal Article