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Annales de l'Institut Henri Poincaré. Analyse non linéaire, ISSN 0294-1449, 11/2016, Volume 33, Issue 6, pp. 1589 - 1638
We prove the existence and the stability of Cantor families of quasi-periodic, small amplitude solutions of quasi-linear (i.e. strongly nonlinear) autonomous... 
Nash–Moser theory | Quasi-periodic solutions | KdV | KAM for PDEs | Quasi-linear PDEs | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Communications in partial differential equations, ISSN 0360-5302, 08/2011, Volume 36, Issue 8, pp. 1353 - 1384
We investigate stable solutions of elliptic equations of the type where n ≥ 2, s ∈ (0, 1), λ ≥0 and f is any smooth positive superlinear function. The operator... 
Boundary reactions | Extremal solutions | Fractional operators | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Partial differential equations | Analysis of PDEs
Journal Article
Communications in mathematical physics, ISSN 0010-3616, 04/2007, Volume 271, Issue 1, pp. 199 - 221
In this paper we consider systems of coupled Schrödinger equations which appear in nonlinear optics. The problem has been considered mostly in the... 
Analysis of PDEs | Mathematics
Journal Article
Archive for rational mechanics and analysis, ISSN 1432-0673, 05/2008, Volume 192, Issue 1, pp. 165 - 186
Journal Article
2012, Mathematical surveys and monographs, ISBN 9780821889817, Volume 183, vii, 317
Book
Annales de l'Institut Henri Poincaré. Analyse non linéaire, ISSN 0294-1449, 01/2014, Volume 31, Issue 1, pp. 23 - 53
This is the first of two articles dealing with the equation (−Δ)sv=f(v) in Rn, with s∈(0,1), where (−Δ)s stands for the fractional Laplacian — the... 
Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Matemàtiques i estadística | Nonlinear teories | Teories no-lineals | Àlgebra | Àrees temàtiques de la UPC | Analysis of PDEs
Journal Article
Asymptotic analysis, ISSN 0921-7134, 01/2019, Volume 115, Issue 1-2, pp. 63 - 94
Subdiffusive motion takes place at a much slower timescale than diffusive motion. As a preliminary step to studying reaction-subdiffusion pulled fronts, we... 
Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Constraining | Mathematics - Analysis of PDEs
Journal Article
Journal of functional analysis, ISSN 0022-1236, 07/2018, Volume 275, Issue 1, pp. 170 - 195
We construct clustering positive solutions for a perturbed critical elliptic equation on a closed manifold of dimension n=4,5. Such a construction is already... 
Blowing-up solutions | Elliptic PDEs | Physical Sciences | Mathematics | Science & Technology | Analysis of PDEs
Journal Article
Duke mathematical journal, ISSN 0012-7094, 06/2019, Volume 168, Issue 8, pp. 1487 - 1537
We study local and global properties of positive solutions of -Delta u = u(p)vertical bar del u vertical bar(q) in a domain Omega of R-N , in the range p + q >... 
Physical Sciences | Mathematics | Science & Technology | Analysis of PDEs
Journal Article
Inventiones mathematicae, ISSN 1432-1297, 12/2007, Volume 171, Issue 3, pp. 485 - 541
We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems,... 
Mathematics, general | Mathematics | Physical Sciences | Science & Technology | Studies | Mathematics - Analysis of PDEs | Analysis of PDEs
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2019, Volume 266, Issue 2-3, pp. 1051 - 1072
The Adimurthi–Druet [1] inequality is an improvement of the standard Moser–Trudinger inequality by adding a L2-type perturbation, quantified by α∈[0,λ1), where... 
Physical Sciences | Mathematics | Science & Technology | Analysis | Equality | Mathematics - Analysis of PDEs | Analysis of PDEs
Journal Article
2010, Oxford mathematical monographs, ISBN 0199541647, Volume 9780199541645, xviii, 411
Generalized dynamic thermoelasticity is a vital area of research in continuum mechanics, free of the classical paradox of infinite propagation speeds of... 
Thermoelasticity | Mathematics | Mathematical and Statistical Physics | Applied Mathematics | Elasticity | Second sound | Wave propagation | Elastodynamics | Hyperbolic pdes | Generalized thermoelasticity
Book
Communications on pure and applied mathematics, ISSN 0010-3640, 10/2016, Volume 69, Issue 10, pp. 1882 - 1923
We establish uniform Lipschitz estimates for second‐order elliptic systems in divergence form with rapidly oscillating, almost‐periodic coefficients. We give... 
Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Homogenization | Dirichlet problem | Analysis of PDEs
Journal Article
Journal of computational physics, ISSN 0021-9991, 08/2012, Volume 231, Issue 20, pp. 6770 - 6789
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 05/2016, Volume 260, Issue 10, pp. 7535 - 7562
In this paper we investigate the inverse problem of determining the time independent scalar potential of the dynamic Schrödinger equation in an infinite... 
Physical Sciences | Mathematics | Science & Technology | Waveguides | Analysis of PDEs
Journal Article