Nicholas D. Alikakos

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Postal address:
Department of Mathematics
University of Athens
15784 Athens
Greece

Short curriculum vitae
Full curriculum vitae


Applied analysis and PDEs seminar

The seminar is taking place online due to the ongoing coronavirus pandemic. Please contact Nick Alikakos for information about attending.

Spring 2021 schedule of talks


Teaching

Applied mathematics lecture notes (in Greek)

Geometric measure theory lecture notes (in Greek)


Research

For a complete list of all published work, see MathSciNet (requires subscription) or zbMATH (free).

Preprints

Lower bounds for the energy and structure properties of minimizers (with G. Fusco)

Existence of free boundaries for entire solutions of the Allen–Cahn system with sub-quadratic potentials (with D. Gazoulis and A. Zarnescu)

A maximum principle for elliptic systems involving the fractional Laplacian (with A. N. Yannacopoulos)

Monograph

Elliptic Systems of Phase Transition Type (with G. Fusco and P. Smyrnelis)
Progress in Nonlinear Differential Equations and Their Applications 91, xii+343 pp. Birkhäuser, Cham, 2018

Video

On the structure of phase transition maps: density estimates and applications
A YouTube video of a talk at the summer school Geometric measure theory and calculus of variations: theory and applications at the Institut Fourier in Grenoble, France

Recent articles

Almost entire solutions of the Burgers equation (with D. Gazoulis)
Electron. J. Differ. Equ. 2018 No. 53, pp. 1–6

Stability criteria for multiphase partitioning problems with volume constraints (with A. Faliagas)
Discrete Contin. Dyn. Syst. 37 No. 2 (2017), pp. 663–683

Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system ΔuWu(u) = 0 (with G. Fusco)
Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 15 Spec. Iss. (2016), pp. 809–836

Density estimates for vector minimizers and applications (with G. Fusco)
Discrete Contin. Dyn. Syst. 35 No.12 (2015), pp. 5631–5663

A maximum principle for systems with variational structure and an application to standing waves (with G. Fusco)
J. Eur. Math. Soc. 17 No. 7 (2015), pp. 1547–1567

On the structure of phase transition maps for three or more coexisting phases
In Geometric partial differential equations, M. Novaga and G. Orlandi eds. pp. 1–31, CRM Series 15, Edizioni della Normale, Pisa, 2013

Plateau angle conditions for the vector-valued Allen–Cahn equation (with P. Antonopoulos and A. Damialis)
SIAM J. Math. Anal. 45 No. 6 (2013), pp. 3823–3837

A new proof for the existence of an equivariant entire solution connecting the minima of the potential for the system ΔuWu(u) = 0
Commun. Partial Differ. Equations 37 No. 12 (2012), pp. 2093–2115

Existence of lattice solutions to semilinear elliptic systems with periodic potential (with P. Smyrnelis)
Electron. J. Differ. Equ. 2012 No. 15 (2012), pp. 1–15

The stress-energy tensor and Pohozaev's identity for systems (with A. C. Faliagas)
Acta Math. Scientia Ser. B, Engl. Ed. 32 No. 1 (2012), pp. 433–439

Entire solutions to equivariant elliptic systems with variational structure (with G. Fusco)
Arch. Ration. Mech. Anal. 202 No. 2 (2011), pp. 567597

On an elliptic system with symmetric potential possessing two global minima (with G. Fusco)
Bull. Greek Math. Soc. 58 (2011), pp. 1–21.

Some basic facts on the system ΔuWu(u) = 0
Proc. Am. Math. Soc. 139 (2011), pp. 153–162

Heteroclinic travelling waves of gradient diffusion systems (with N. I. Katzourakis)
Trans. Am. Math. Soc. 363 (2011), pp. 1362–1397

A replacement lemma for obtaining pointwise estimates in phase transition models (with G. Fusco)
Unpublished preprint

Entire solutions to nonconvex variational elliptic systems in the presence of a finite symmetry group (with G. Fusco)
In Singularities in nonlinear evolution phenomena and applications, M. Novaga and G. Orlandi eds. pp. 1–26, CRM Series 9, Edizioni della Normale, Pisa, 2009

On the connection problem for potentials with several global minima (with G. Fusco)
Indiana Univ. Math. J. 57 No. 4 (2008), pp. 1871–1906

Singular perturbation problems arising from the anisotropy of crystalline grain boundaries (with P. C. Fife, G. Fusco, and Ch. Sourdis)
J. Dyn. Differ. Equations 19 No. 4 (2007), pp. 935–949

Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries (with P. C. Fife, G. Fusco, and Ch. Sourdis)
Interfaces Free Bound. 8 No. 2 (2006), pp. 159–183

Explicit stationary solutions in multiple well dynamics and non-uniqueness of interfacial energy densities (with S. I. Betelú and X. Chen)
Eur. J. Appl. Math. 17 No. 5 (2006), pp. 525–556

Analysis of a corner layer problem in anisotropic interfaces (with P. W. Bates, J. W. Cahn, P. C. Fife, G. Fusco, and G. B. Tanoglu)
Discrete Contin. Dyn. Syst. Ser. B 6 No. 2 (2006), pp. 237–255

Ostwald ripening in two dimensions—the rigorous derivation of the equations from the Mullins–Sekerka dynamics (with G. Fusco and G. Karali)
J. Differ. Equations 205 No. 1 (2004), pp. 1–49

Continuum limits of particles interacting via diffusion (with G. Fusco and G. Karali)
Abstr. Appl. Anal. 3 (2004), pp. 215–237

Motion of bubbles towards the boundary for the Cahn–Hilliard equation (with G. Fusco and G. Karali)
Eur. J. Appl. Math. 15 No. 1 (2004), pp. 103–124

The effect of the geometry of the particle distribution in Ostwald ripening (with G. Fusco and G. Karali)
Commun. Math. Phys. 238 No. 3 (2003), pp. 481–488

Ostwald ripening for dilute systems under quasistationary dynamics (with G. Fusco)
Commun. Math. Phys. 238 No. 3 (2003), pp. 429–479

The normalized mean curvature flow for a small bubble in a Riemannian manifold (with A. Freire)
J. Differ. Geom. 64 No. 2 (2003), pp. 247–303

The effect of distribution in space in Ostwald ripening (with G. Fusco)
In Nonlinear dynamics and renormalization group, I. M. Sigal and C. Sulem eds. pp. 17–28, CRM Proc. Lect. Notes. 27, American Mathematical Society, Providence, RI, 2001

Motion of a droplet by surface tension along the boundary (with X. Chen and G. Fusco)
Calc. Var. Partial Differ. Equ. 11 No. 3 (2000), pp. 233–305

Mullins–Sekerka motion of small droplets on a fixed boundary (with P. W. Bates, X. Chen, and G. Fusco)
J. Geom. Anal. 10 No. 4 (2000), pp. 575–596

Last modified on April 2, 2021