03/2020

The goal of the paper is to develop a method that will combine the use of variational techniques with regularization methods in order to study existence and...

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 03/2020, Volume 135, pp. 256 - 283

We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, associated with the Neumann Laplacian in a box Ω⊂RN, which...

Mixed Neumann-Dirichlet boundary conditions | Isoperimetric profile | Concentration phenomena | Singular limits | α-symmetrization | Survival threshold

Mixed Neumann-Dirichlet boundary conditions | Isoperimetric profile | Concentration phenomena | Singular limits | α-symmetrization | Survival threshold

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 12/2019, Volume 72, Issue 12, pp. 2578 - 2620

This paper describes the structure of the nodal set of segregation profiles arising in the singular limit of planar, stationary, reaction‐diffusion systems...

Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

10/2019

We prove the existence of solutions $(\lambda, v)\in \mathbb{R}\times H^{1}(\Omega)$ of the elliptic problem \[ \begin{cases} -\Delta v+(V(x)+\lambda) v...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

5.
Full Text
Local minimizers in absence of ground states for the critical NLS energy on metric graphs

09/2019

We consider the mass-critical nonlinear Schr\"odinger equation on non-compact metric graphs. A quite complete description of the structure of the ground...

Journal Article

03/2019

We analyze the fundamental solution of a time-fractional problem, establishing existence and uniqueness in an appropriate functional space. We also focus on...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

Nonlinearity, ISSN 0951-7715, 02/2019, Volume 32, Issue 3, pp. 1044 - 1072

We analyze L-2-normalized solutions of nonlinear Schrodinger systems of Gross-Pitaevskii type, on bounded domains, with homogeneous Dirichlet boundary...

Gross-Pitaevskii systems | critical exponents | solitary waves | orbital stability | constrained critical points | EXISTENCE | MATHEMATICS, APPLIED | HOLDER BOUNDS | POSITIVE SOLUTIONS | EQUATIONS | STANDING WAVES | PHYSICS, MATHEMATICAL | SUPERCRITICAL NLS | CONVERGENCE | GROUND-STATES

Gross-Pitaevskii systems | critical exponents | solitary waves | orbital stability | constrained critical points | EXISTENCE | MATHEMATICS, APPLIED | HOLDER BOUNDS | POSITIVE SOLUTIONS | EQUATIONS | STANDING WAVES | PHYSICS, MATHEMATICAL | SUPERCRITICAL NLS | CONVERGENCE | GROUND-STATES

Journal Article

8.
Full Text
Quantitative analysis of a singularly perturbed shape optimization problem in a polygon

02/2019

We carry on our study of the connection between two shape optimization problems with spectral cost. On the one hand, we consider the optimal design problem for...

Journal Article

11/2018

We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, associated with the Neumann Laplacian in a box...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

Mathematics in Engineering, 10/2018, Volume 1, Issue 1, pp. 147 - 173

In this paper we construct a viscosity solution of a two-phase free boundary problem for a class of fully nonlinear equation with distributed sources, via an...

Perron method| two-phase free boundary problems| fully nonlinear elliptic equations

Perron method| two-phase free boundary problems| fully nonlinear elliptic equations

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2018, Volume 370, Issue 10, pp. 7149 - 7179

We prove that the planar hexagonal honeycomb is asymptotically optimal for a large class of optimal partition problems, in which the cells are assumed to be...

Logarithmic capacity | Discrete faber-krahn inequality | Cheeger constant | Honeycomb conjecture | Optimal partitions | MATHEMATICS | EIGENVALUES | logarithmic capacity | discrete Faber-Krahn inequality | INEQUALITY | honeycomb conjecture | N-GONS | Analysis of PDEs | Mathematics

Logarithmic capacity | Discrete faber-krahn inequality | Cheeger constant | Honeycomb conjecture | Optimal partitions | MATHEMATICS | EIGENVALUES | logarithmic capacity | discrete Faber-Krahn inequality | INEQUALITY | honeycomb conjecture | N-GONS | Analysis of PDEs | Mathematics

Journal Article

07/2018

We analyze $L^2$-normalized solutions of nonlinear Schr\"odinger systems of Gross-Pitaevskii type, on bounded domains, with homogeneous Dirichlet boundary...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 5/2018, Volume 76, Issue 6, pp. 1357 - 1386

We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the...

Secondary 35P15 | Periodic environments | 92D25 | Mathematical and Computational Biology | Survival threshold | Mathematics | 47A75 | Applications of Mathematics | Primary 35R11 | Spectral fractional Laplacian | Reflecting barriers | DIFFUSIVE LOGISTIC EQUATIONS | BOUNDARY-CONDITIONS | DISRUPTED ENVIRONMENTS | ANOMALOUS DIFFUSION | MODELS | SPECIES PERSISTENCE | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | FRONT DYNAMICS | WEIGHT | POPULATION-DYNAMICS | LEVY | Eigenvalues | Boundary value problems | Research | Mathematical research | Laplacian operator | Diffusion | Survival | Dispersal | Optimization | Eigen values

Secondary 35P15 | Periodic environments | 92D25 | Mathematical and Computational Biology | Survival threshold | Mathematics | 47A75 | Applications of Mathematics | Primary 35R11 | Spectral fractional Laplacian | Reflecting barriers | DIFFUSIVE LOGISTIC EQUATIONS | BOUNDARY-CONDITIONS | DISRUPTED ENVIRONMENTS | ANOMALOUS DIFFUSION | MODELS | SPECIES PERSISTENCE | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | FRONT DYNAMICS | WEIGHT | POPULATION-DYNAMICS | LEVY | Eigenvalues | Boundary value problems | Research | Mathematical research | Laplacian operator | Diffusion | Survival | Dispersal | Optimization | Eigen values

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2017, Volume 56, Issue 5, pp. 1 - 27

Given $$\rho >0$$ ρ > 0 , we study the elliptic problem $$\begin{aligned} \text {find } (U,\lambda )\in H^1_0(\Omega )\times {\mathbb {R}}\text { such that }...

35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35Q55 | Mathematics | 35C08 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SUPERCRITICAL NLS | MORSE INDEX | STANDING WAVES | UNBOUNDED-DOMAINS | ORBITAL STABILITY | CRITICAL-POINTS

35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35Q55 | Mathematics | 35C08 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SUPERCRITICAL NLS | MORSE INDEX | STANDING WAVES | UNBOUNDED-DOMAINS | ORBITAL STABILITY | CRITICAL-POINTS

Journal Article

ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 07/2017, Volume 23, Issue 3, pp. 1145 - 1177

We search for non-constant normalized solutions to the semilinear elliptic system {-v Delta v(i) + g(i) (v(j)(2))v(i) =lambda(i)v(i,) v(i) > 0 in Omega partial...

Singularly perturbed problems | Normalized solutions to semilinear elliptic systems | Multi-population differential games | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | FREE-BOUNDARIES | HOLDER BOUNDS | normalized solutions to semilinear elliptic systems | multi-population differential games | BEHAVIOR | POPULATIONS | STRONGLY COMPETING SYSTEMS | MODELS | MASS | ELLIPTIC-SYSTEMS | DOMAINS | AUTOMATION & CONTROL SYSTEMS | Bifurcations | Populations | Variational methods | Game theory | Differential games

Singularly perturbed problems | Normalized solutions to semilinear elliptic systems | Multi-population differential games | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | FREE-BOUNDARIES | HOLDER BOUNDS | normalized solutions to semilinear elliptic systems | multi-population differential games | BEHAVIOR | POPULATIONS | STRONGLY COMPETING SYSTEMS | MODELS | MASS | ELLIPTIC-SYSTEMS | DOMAINS | AUTOMATION & CONTROL SYSTEMS | Bifurcations | Populations | Variational methods | Game theory | Differential games

Journal Article

03/2017

We prove that the planar hexagonal honeycomb is asymptotically optimal for a large class of optimal partition problems, in which the cells are assumed to be...

Mathematics - Optimization and Control

Mathematics - Optimization and Control

Journal Article

07/2016

J. Math. Biol. (2018) 76:1357--1386 We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian....

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

07/2016

Given $\rho>0$, we study the elliptic problem \[ \text{find } (U,\lambda)\in H^1_0(\Omega)\times \mathbb{R} \text{ such that } \begin{cases} -\Delta U+\lambda...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 12, pp. 2865 - 2924

For a class of competition-diffusion nonlinear systems involving the square root of the laplacian, including the fractional Gross-Pitaevskii system....

Singular perturbations | Optimal regularity of limiting profiles | Strongly competing systems | Square root of the laplacian | Spatial segregation | OBSTACLE PROBLEM | singular perturbations | MATHEMATICS, APPLIED | FREE-BOUNDARIES | SEGREGATION | optimal regularity of limiting profiles | CONJECTURE | FRACTIONAL LAPLACIAN | MATHEMATICS | REGULARITY | spatial segregation | ELLIPTIC-SYSTEMS | DIFFUSION | strongly competing systems

Singular perturbations | Optimal regularity of limiting profiles | Strongly competing systems | Square root of the laplacian | Spatial segregation | OBSTACLE PROBLEM | singular perturbations | MATHEMATICS, APPLIED | FREE-BOUNDARIES | SEGREGATION | optimal regularity of limiting profiles | CONJECTURE | FRACTIONAL LAPLACIAN | MATHEMATICS | REGULARITY | spatial segregation | ELLIPTIC-SYSTEMS | DIFFUSION | strongly competing systems

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 12/2015, Volume 35, Issue 12, pp. 6085 - 6112

For the cubic Schrodinger system with trapping potentials in R-N, N <= 3, or in bounded domains, we investigate the existence and the orbital stability of...

Orbital stability | Gross-Pitaevskii systems | Ambrosetti-Prodi type problem | Cooperative and competitive elliptic systems | Constrained critical points | EXISTENCE | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | EQUATIONS | STANDING WAVES | MATHEMATICS | R-N | SYMMETRY | BOUND-STATES | constrained critical points | orbital stability | DOMAINS

Orbital stability | Gross-Pitaevskii systems | Ambrosetti-Prodi type problem | Cooperative and competitive elliptic systems | Constrained critical points | EXISTENCE | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | EQUATIONS | STANDING WAVES | MATHEMATICS | R-N | SYMMETRY | BOUND-STATES | constrained critical points | orbital stability | DOMAINS

Journal Article

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