Nicholas D. Alikakos

E-mail address:

Postal Address:
Department of Mathematics
University of Athens
GR-15784, Athens
Greece

Short curriculum vitae

Geometric Measure Theory Lecture Notes

NEW!A brief introduction into the Q-tensor theory of liquid crystals by Prof. Arghir Zarnescu Lecture 1, Lecture 2

NEW! Spring 2015 Seminars (by K. Smoczyk, H. Brezis, B. Dacorogna, G. Fusco, P. Bates)

Fall 2014 Seminars

Four lectures on mass transfer, a mini course offered by F. Santambrogio

Spring 2014 Seminars (by G. Barbatis, T. Bourni, M. Kowalczyk, F. Santambrogio, A. Aftalion, G. Akrivis)

Fall 2013 Seminars (by F. Santambrogio, G. Fusco, P. Sternberg, M. Novaga, G. Papanicolaou)

Workshop on Recent Advances in Nonlinear PDE and Calculus of Variations 12–14 February, 2014, Reading, UK

FIRST Workshop on Reaction-Diffusion Systems with Gradient Structure, University of Athens, March 18–21, 2013.

Two graduate student fellowships in PDE available. Contact: Prof. N. Alikakos

Winter 2014–2015 classes & seminars

Applied Analysis and PDEs Seminar

Spring 2014 classes & seminars

Applied Analysis and PDEs Seminar

EM.07 Συνήθεις Διαφορικές Εξισώσεις - Δυναμικά Συστήματα: Διάλεξη 1, Διάλεξη 1 (Τελευταίες σελίδες), Διάλεξη 2, Διάλεξη 3

EM.14 Μη Γραμμική Ανάλυση και Λογισμός Μεταβολών: Βιβλίο, Διάλεξη 3, Διάλεξη 4, Διάλεξη 5

Spring 2013 classes & seminars

Applied Analysis and PDEs Seminar

Geometric evolution equations, a course offered by Prof. Klaus Ecker (Freie Universität Berlin)

Winter 2012–13 classes & seminars

Applied Analysis and PDEs Seminar

EM.01 Μέθοδοι Εφαρμοσμένων Μαθηματικών Ι: Το θεώρημα πεπλεγμένης συνάρτησης, Μη γραμμική διαφόριση, Η αρχή του σταθερού σημείου

EM.14 Μη Γραμμική Ανάλυση και Λογισμός Μεταβολών: Πληροφορίες, Διάλεξη 1, Διάλεξη 2, Διάλεξη 3, Διάλεξη 4, Διάλεξη 5, Διάλεξη 6, Διάλεξη 7, Διάλεξη 8, Διάλεξη 9, Διάλεξη 10, Διάλεξη 11, Διάλεξη 12, Διάλεξη 13, Διάλεξη 14, Διαφορική γεωμετρία, Διάλεξη 15, Διάλεξη 16, Διάλεξη 17, Διάλεξη 18

Winter 2011–12 classes & seminars

Applied Analysis and PDEs Seminar

EM.01 Μέθοδοι Εφαρμοσμένων Μαθηματικών Ι

Μαθηματικά για φοιτητές Πληροφορικής

Εφαρμοσμένη Συναρτησιακή Ανάλυση: Διάλεξη 1, Διάλεξη 2, Διάλεξη 3, Διάλεξη 4, Διάλεξη 5

Spring 2011 classes & seminars

Applied Analysis and PDEs Seminar

411 Μερικές Διαφορικές Εξισώσεις Ι (συνδιδασκαλία με Χ. Ε. Αθανασιάδη): Σημειώσεις.

Dynamics in Samos 2010, Karlovassi, Samos, Greece, 31 August – 3 September 2010

Modern Mathematical Methods in Science and Technology ’09, Poros, Greece, 3–5 September 2009

Mathematical Challenges Motivated by Multiphase Materials: Analytical, Stochastic and Discrete Aspects, Anogia, Crete, Greece, 21–16 June 2009

Workshop on Stochastic and Deterministic Models, Athens, Greece, 21–22 November 2008

Panhellenic Conference in Mathematical Analysis, Athens, Greece, 15–17 May 2008

Recent publications

(For a list of all publications, see the full curriculum vitae.)

Almost Entire Solutions of the Burgers Equation (with D. Gazoulis)
Electr. J. Differential Equations Vol 2018 No. 53 (2018) pp. 1–6

Elliptic Systems of Phase Transition Type (with G. Fusco and P. Smyrnelis)
Monograph in the series Progress in Nonlinear Differential Equations and Their Applications, Birkhauser (2018)

Density estimates for vector minimizers and applications (with G. Fusco)
Discrete and continuous dynamical systems 35 No.12, pp. 5631–5663 (2015), Special issue edited by E.Valdinoci.

Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system Δu − W_u(u) = 0 (with G. Fusco)
Annali della Scuola Normale Superiore di Pisa, XV issue special, pp. 809–836 (2016)

A maximum principle for systems with variational structure and an application to standing waves (with G. Fusco)
Journal of the European Mathematical Society 17 No.7 pp. 1547–1567 (2015)

On the structure of phase transition maps for three or more coexisting phases
In Geometric partial differential equations, M. Novaga and G. Orlandi eds. Publications of the Scuola Normale Superiore, CRM Series, Birkhäuser, 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 Δu − W_u(u) = 0
Comm. Partial Diff. Eqs 37 No. 12 (2012) pp. 2093–2115

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

Existence of lattice solutions to semilinear elliptic systems with periodic potential (with P. Smyrnelis)
Electr. J. Diff. Equations 2012 No. 15 (2012) pp. 1–15

The stress-energy tensor and Pohozaev's identity for systems (with A. Faliagas)
Acta Math. Scientia 32 No. 1 (2012) pp. 433–439 (For a preprint version, click here)

Entire solutions to equivariant elliptic systems with variational structure (with G. Fusco)
Arch. Rat. Mech. Anal. 202 No. 2 (2011) pp. 567–597

On an elliptic system with symmetric potential possessing two global minima (with G. Fusco)
To appear in Bull. Greek Math. Soc.

Some basic facts on the system Δu − W_u(u) = 0
Proc. Amer. Math. Soc. 139 (2011) pp. 153–162

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

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. Publications of the Scuola Normale Superiore, CRM Series, Birkhäuser, 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. Fife, G. Fusco, and Ch. Sourdis)
J. Dyn. Diff. 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. 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. 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. Bates, J. Cahn, P. Fife, G. Fusco, and G. 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. Diff. 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)
Comm. Math. Phys. 238 No. 3 (2003) pp. 481–488

Ostwald ripening for dilute systems under quasistationary dynamics (with G. Fusco)
Comm. 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. Diff. Geom. 64 No. 2 (2003) pp. 247–303

Last modified on 18 November 2014

Nicholas D. Alikakos

Winter 2014–2015 classes & seminars

Spring 2014 classes & seminars

Spring 2013 classes & seminars

Winter 2012–13 classes & seminars

Winter 2011–12 classes & seminars

Spring 2011 classes & seminars

Winter 2010–11 classes & seminars

Spring 2010 classes & seminars

Winter 2009–10 classes & seminars

Organization of recent and forthcoming conferences

Recent publications