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09/2018, 1, ISBN 1498746160, 294
The fractional Laplacian, also called the Riesz fractional derivative, describes an unusual diffusion process associated with random excursions. The Fractional... 
Mathematics | Laplacian operator | Mathematics & Statistics for Engineers | Applied Mathematics | Computational Numerical Analysis | Fractional calculus
eBook
Advances in Mathematics, ISSN 0001-8708, 2011, Volume 226, Issue 2, pp. 1410 - 1432
In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of... 
Fractional Laplacian | Dirichlet-to-Neumann operators | Asymptotically hyperbolic manifolds | Conformally covariant operators | Conformal geometry | MATHEMATICS | REGULARITY | RESOLVENT | METRICS | EXTENSION | Manifolds (Mathematics) | Matemàtiques i estadística | Geometria diferencial | Àrees temàtiques de la UPC | Laplacian operator
Journal Article
Revista Matematica Iberoamericana, ISSN 0213-2230, 2016, Volume 32, Issue 4, pp. 1353 - 1392
By virtue of barrier arguments we prove C-alpha-regularity up to the boundary for the weak solutions of a non-local, non-linear problem driven by the... 
Fractional p-Laplacian | Global Hölder regularity | Fractional Sobolev spaces | fractional Sobolev spaces | MATHEMATICS | SOBOLEV SPACES | global Holder regularity | INTEGRODIFFERENTIAL EQUATIONS | BOUNDARY | OPERATORS
Journal Article
Advances in Nonlinear Analysis, ISSN 2191-9496, 02/2015, Volume 4, Issue 1, pp. 13 - 23
We study the Dancer–Fučík spectrum of the fractional -Laplacian operator. We construct an unbounded sequence of decreasing curves in the spectrum using a... 
Dancer–Fučík spectrum | 35A15 | critical groups | 35R11 | Fractional | 35P30 | Laplacian | Fractional p-Laplacian | Dancer-Fučík spectrum | Critical groups | MATHEMATICS | MATHEMATICS, APPLIED | Dancer-Fucik spectrum | MULTIPLE-EIGENVALUES | BOUNDARY-VALUE-PROBLEMS | DIRICHLET PROBLEM | JUMPING NONLINEARITIES | NONRESONANCE
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2011, Volume 42, Issue 1, pp. 21 - 41
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 4, pp. A2383 - A2405
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the... 
Numerical approximation | Finite element–spectral method | Fractional laplacian | finite element-spectral method | MATHEMATICS, APPLIED | fractional laplacian | numerical approximation | ELLIPTIC-OPERATORS | EXTENSION PROBLEM | Mathematics - Numerical Analysis | MATHEMATICS AND COMPUTING
Journal Article
JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 0022-0396, 10/2013, Volume 255, Issue 8, pp. 2340 - 2362
We study the existence and multiplicity of solutions for elliptic equations in RN, driven by a non-local integro-differential operator, which main prototype is... 
INDEFINITE | MATHEMATICS | Variational methods | LOCAL SUPERLINEARITY | SUBLINEARITY | REGULARITY | CONCAVE | NONLINEARITIES | EQUATION | Existence | Fractional Sobolev spaces
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 04/2016, Volume 36, Issue 4, pp. 1813 - 1845
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 | MATHEMATICS | best critical Sobolev constant | INEQUALITIES | variational techniques | fractional Laplacian | critical non-linearities | integrodifferential operators
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2016, Volume 260, Issue 2, pp. 1392 - 1413
The purpose of this paper is to investigate the existence of weak solutions for a perturbed nonlinear elliptic equation driven by the fractional -Laplacian... 
Fractional p-Laplacian | Fractional Schrödinger equation | Mountain pass theorem | Variational methods | 35A15 | 47G20 | 35J60 | 35R11 | MATHEMATICS | ELLIPTIC PROBLEMS | CONCAVE | SCHRODINGER-EQUATION | NONLINEARITIES | Fractional Schrodinger equation
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 07/2017, Volume 263, Issue 1, pp. 765 - 778
Our propose here is to provide a Hopf lemma and a strong minimum principle for weak supersolutions of where Ω is an open set of , , , and is the fractional... 
Fractional p-Laplacian | Hopf's lemma | Strong minimum principle | MATHEMATICS | Mathematics - Analysis of PDEs
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2017, Volume 308, pp. 404 - 437
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 02/2016, Volume 27, pp. 80 - 92
In this article, we are concerned with the multiplicity of solutions to the following fractional p-Laplacian system where is a smooth bounded set in , with... 
Nehari manifold | Fibering maps | Fractional p-Laplacian system | Concave–convex nonlinearities | Concave-convex nonlinearities | MATHEMATICS, APPLIED | INEQUALITIES | BREZIS-NIRENBERG RESULT | EQUATIONS | DRIVEN | ELLIPTIC SYSTEM | WEIGHT | OPERATORS | MULTIPLE POSITIVE SOLUTIONS | Manifolds | Nonlinearity | Operators | Exponents | Images
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 08/2007, Volume 32, Issue 8, pp. 1245 - 1260
The operator square root of the Laplacian (− ▵) 1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the... 
Fractional Laplacian | 35J70 | 26A33 | Degenerate elliptic equations | MATHEMATICS | MATHEMATICS, APPLIED | degenerate elliptic equations | DEGENERATE ELLIPTIC-EQUATIONS | fractional Laplacian | Mathematics - Analysis of PDEs
Journal Article
Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 14
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 09/2014, Volume 39, Issue 9, pp. 1780 - 1790
We compare two natural types of fractional Laplacians (− Δ) s , namely, the "Navier" and the "Dirichlet" ones. We show that for 0 < s < 1 their difference is... 
Fractional Laplacian | Sobolev constant | Nonlocal differential operators | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS | EXTENSION PROBLEM | Partial differential equations | Dirichlet problem | Constants | Preserving | Fluid flow
Journal Article
Advances in Calculus of Variations, ISSN 1864-8258, 04/2016, Volume 9, Issue 2, pp. 101 - 125
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 06/2016, Volume 105, Issue 6, pp. 810 - 844
In this paper we study the fractional -Laplacian evolution equation given by , . In a bounded domain Ω we deal with the Dirichlet problem by taking and in ,... 
Neumann problem | Dirichlet problem | p-Laplacian | Fractional Sobolev spaces | Cauchy problem | P-Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | INEQUALITIES | CONVERGENCE
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 10/2013, Volume 255, Issue 8, pp. 2340 - 2362
We study the existence and multiplicity of solutions for elliptic equations in , driven by a non-local integro-differential operator, which main prototype is... 
Variational methods | Existence | Fractional Sobolev spaces
Journal Article
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