New work on elliptic regularity and variational models
Recent preprints are listed in the publications section.
ACADEMIC PROFILE NAPLES, ITALY
Mathematical analysis
and its applications.
My research uses variational techniques to investigate mathematical problems arising in continuum mechanics and materials science.
I am particularly interested in magnetic skyrmions, liquid crystals and thin structures, as well as nonlinear partial differential equations and functional inequalities.
Calculus of variationsPartial differential equationsMathematical materials science
01 / ACADEMIC HIGHLIGHTS
Selected activities
↗
Invited speaker · Isaac Newton Institute, Cambridge
Recent challenges in the mathematical design of new materials.
Analysis and Modeling of Magnetic Skyrmions
FWF research project P34609 · Principal Investigator (ended October 2025).
Co-supervision of two PhD students at TU Wien
Together with Elisa Davoli · Rossella Giorgio and Leon Happ.
02 / LATEST WORK
Recent publications
03 / TEACHING
This academic year
2026 / 27Calculus IElectrical Engineering and Information Technology
2026 / 27Mathematical Analysis IICivil and Environmental Engineering
RESEARCH AREAS
Research
My work is at the interface of rigorous mathematical analysis and the modelling of physical phenomena, particularly in continuum mechanics and materials science.
SELECTED FOCUS
The mathematics of magnetic skyrmions
I investigate variational models for magnetic textures, chirality, thin films and the geometry of energy minimisers, with analytical and numerical approaches.
Related paper on ResearchGate01
Micromagnetics and magnetic textures
Equilibrium states, skyrmions, nonlocal magnetostatic interactions, the Dzyaloshinskii–Moriya interaction, and reduced models for thin magnetic structures.
02
Partial differential equations and inequalities
Regularity of nonlinear elliptic systems, harmonic maps, symmetry of minimisers, and functional inequalities in classical and variable-exponent spaces.
03
Nonlocal variational models and soft matter
Nonlocal-to-local limits, calculus of variations for liquid crystals, dimensional reduction, and analytical questions from continuum mechanics.
RESEARCH PROJECT
Analysis and Modeling of Magnetic Skyrmions
FWF project P34609 (2022–2025) · Principal Investigator. Research on magnetic skyrmions, micromagnetics and variational methods.
FWF
P34609
P34609
RESEARCH OUTPUT
Publications
Complete bibliography from my publication list, with recent 2026 additions. Select a year or category, or search by title, author and subject. Paper titles link to their ResearchGate records where available.
Reduced energies for thin ferromagnetic films with perpendicular anisotropy
Mathematical Models and Methods in Applied Sciences, 34(10), 1861–1904Journal articleResearchGateDOI ↗
Sharp conditions for the validity of the Bourgain–Brezis–Mironescu formula
Proceedings of the Royal Society of Edinburgh, Section A: MathematicsJournal articleResearchGateDOI ↗
Adaptive Uzawa algorithm for the Stokes equation
ESAIM: Mathematical Modelling and Numerical Analysis, 53(6), 1841–1870Journal articleResearchGateDOI ↗
Liouville type results for local minimizers of the micromagnetic energy
Calculus of Variations and Partial Differential Equations, 53(3–4), 525–560Journal articleResearchGateDOI ↗
Schemi sulla teoria della misura e dell’integrazione
No matching publications.
Bibliography based on the author’s publication list (45 entries), with three newer 2026 preprints. Journal metadata and DOI corrections checked against publishers and institutional records.
BEYOND PUBLICATIONS
Activities
Supervision, press, organised events, invited talks, funding and service to the research community.
01 / SUPERVISION
Doctoral students
At TU Wien I co-supervised two PhD students together with Elisa Davoli, head of the Multiscale Calculus of Variations group. Both were members of the FWF project “Analysis and Modeling of Magnetic Skyrmions”.
Rossella Giorgio — completed her PhD at TU Wien in 2026 with a thesis on nonlocal variational problems and their applications to micromagnetics. TU Wien announcement ↗
Leon Happ — completed his PhD at TU Wien with the thesis “Modern phenomena in micromagnetics from a variational point of view”, on manifold-valued homogenization in micromagnetics. Personal page ↗
02 / IN THE MEDIA
Press and outreach
Für innovative Datenspeicher
Giovanni Di Fratta berechnet Materialstrukturen
A feature in the Austrian weekly Falter on my research on magnetic skyrmions, and on how mathematics can help predict their stability and dynamics for future energy-saving data storage.
Read the article (German)03 / ORGANISATION
Organised events
2021
Nanomagnetism: Analysis, Modeling, Simulation, Experiments
Minisymposium within the SIAM Conference on Mathematical Aspects of Materials Science (17–28 May 2021) · co-organised with C. Muratov and V. Slastikov.
2019
New Trends in the Variational Modeling and Simulation of Liquid Crystals
Workshop at the Erwin Schrödinger Institute, Vienna (2–6 December 2019) · co-organised with M. Ruggeri, V. Slastikov and A. Zarnescu · €14,400 funding.
04 / INVITED TALKS
Selected invited talks
2025
Isaac Newton Institute, University of Cambridge — workshop “Recent challenges in the mathematical design of new materials”
2024
University of Parma — “Modeling and Analysis in Nanomagnetism and Beyond”
Minimizing micromagnetic maps with axial symmetry
2024
University of Naples Federico II — “Variational Methods in Materials Science, II”
Minimizing micromagnetic maps with axial symmetry
2023
TU Wien — 13th International Symposium on Hysteresis Modeling and Micromagnetics (HMM 2023)
Curved thin-film limits of chiral Dirichlet energies
2023
Hausdorff Research Institute for Mathematics, Bonn — “Current Challenges in Complex Materials: Modelling and Analysis”
Curved thin-film limits of chiral Dirichlet energies
2021
Accademia Nazionale dei Lincei — “New and Old Function Spaces in the Theory of PDEs and Nonlinear Analysis”
A unified divergent approach to Hardy–Poincaré inequalities in classical and variable Sobolev spaces
2021
SIAM Conference on Mathematical Aspects of Materials Science — “Mathematical Analysis of Soft Materials”
A unified divergent approach to Hardy–Poincaré inequalities in classical and variable Sobolev spaces
2021
Online North East PDE and Analysis Seminar (ONEPAS) — “The Mathematics of Thin Structures”
Micromagnetics of curved thin films
2019
Isaac Newton Institute, Cambridge — programme “The Mathematical Design of New Materials”
Magnetic skyrmions in spherical thin films
2016
SIAM Conference on Mathematical Aspects of Materials Science, Philadelphia — “Recent Trends in Micromagnetic Modeling and Analysis”
Homogenization of composite ferromagnetic materials
More invited seminars
- 2021Applied Analysis Seminar, Universität BremenVariational theory of magnetic skyrmions
- 2021PDE Afternoon, Universität WienA unified divergent approach to Hardy–Poincaré inequalities in classical and variable Sobolev spaces
- 2018Seminario di Analisi Matematica, Università di Napoli Federico IIVariational Analysis of Magnetic Skyrmions
- 2018DK Winter Workshop and SFB Internal Meeting, Reichenau an der RaxThe micromagnetic energy functional on curved thin films
- 2016Oberseminar Analysis, RWTH Aachen UniversityOn a sharp Poincaré-type inequality on the 2-sphere
- 2016Séminaire du CMAP, École PolytechniqueLiouville type results for local minimizers of the micromagnetic energy
- 2014Micromagnétisme: Mathématiques Appliquées et Nouvelles Interactions Physiques, GrenobleHomogenization of composite ferromagnetic material
- 2014Mathematical Analysis Seminar, University of BristolThe Newtonian Potential and the Demagnetizing Factors of the General Ellipsoid
05 / FUNDING
Grants and fellowships
Current
FRA Project-B · VarMoCry — Variational analysis and modeling of liquid crystals
Co-proponent, together with Bianca Stroffolini and Giovanni Scilla · University of Naples Federico II research funding (FRA).
2022–25
FWF P34609 · Analysis and Modeling of Magnetic Skyrmions
Project leader and Principal Investigator · Austrian Science Fund (FWF) · competitive, peer-reviewed call · ended October 2025.
€323,358↗
2023 —
PRIN2022 · Variational analysis of complex systems in materials science, physics and biology
Project member · Italian Ministry of University and Research (MUR) · grant 2022HKBF5C.
2017–21
SFB65 · Taming Complexity in Partial Differential Systems
Project member · Austrian Science Fund (FWF) Special Research Programme.
2014–16
FMJH Postdoctoral Fellowship
Fondation Mathématique Jacques Hadamard · Labex LMH (ANR-11-LABX-0056-LMH) · two years, competitive and peer-reviewed.
06 / OTHER ACTIVITIES
Research stays and qualifications
2023
Invited and funded participant, trimester programme “Mathematics for Complex Materials”
Hausdorff Research Institute for Mathematics, Bonn
2020
Habilitation and Privatdozent title, TU Wien
Thesis “Variational Methods in the Study of Ferromagnetic Materials”, defended 23 November 2020.
2020
Invited guest, Max Planck Institute for Mathematics in the Sciences
Leipzig, Germany.
2019
Invited and funded participant, programme “The Mathematical Design of New Materials”
Isaac Newton Institute, University of Cambridge · 21 April – 14 June 2019.
2014
Alumni member, Cité Internationale Universitaire de Paris
Elected by competitive selection on qualifications.
2009–10
Ranked first, PhD in Mathematics for Engineering Sciences (XXV cycle)
Politecnico di Torino
07 / SERVICE
Editorial and refereeing
—
Academic Editor, Journal of Function Spaces
Member of the editorial board (Hindawi).
2021
Scientific expert, Agence Nationale de la Recherche (ANR)
Selected for the evaluation of the 2021 Generic Call.
REFEREE FOR
Calculus of Variations and Partial Differential EquationsJournal of Nonlinear ScienceNature CommunicationsAnnales Academiæ Scientiarum FennicæActa Applicandae MathematicaeDifferential and Integral EquationsJournal of Function SpacesSIAM Journal on Mathematical AnalysisSIAM Journal on Applied Mathematics
UNIVERSITY TEACHING
Teaching
Current and previous teaching at the University of Naples Federico II and TU Wien. For official syllabi and announcements, consult the faculty portal.
CURRENT COURSES · 2026 / 2027
University of Naples Federico II
2026 / 27
Calculus I
Electrical Engineering and Information Technology (DM3) · University of Naples Federico II
Current assignments are based on the 2026/27 university teaching listing.
PREVIOUS TEACHING
Naples
2025 / 26
Mathematical Analysis I
Civil, Building and Environmental Engineering · 9 ECTS
2025 / 26
Mathematical Analysis I
Electrical, Naval and Environmental Engineering · 9 ECTS
2024 / 25
Mathematical Analysis I
Engineering programmes (Civil, Building, Environmental, Electrical and Naval)
2021 / 22
Mathematical Analysis II
Civil, Building and Environmental Engineering · 9 ECTS
TEACHING IN VIENNA
TU Wien
2018 / 2019 / 2020
Theory of Distributions
Master’s and doctoral students in Technical Mathematics · 3 ECTS
2020 / 2021
Scientific Programming in Mathematics
MSc in Mathematical Modelling in Engineering · 3 ECTS
ACADEMIC BACKGROUND
Academic CV
Research and university appointments in Italy, Austria, Spain, France and the United Kingdom.
EXPERIENCE
Academic appointments
2024 —
Professor of Mathematical Analysis
University of Naples Federico II · Naples, Italy
2021–24
Researcher in Mathematical Analysis
University of Naples Federico II · Naples, Italy
2017–21
University Assistant / Privatdozent
TU Wien · Vienna, Austria
2016–17
Visiting Fellow
Basque Center for Applied Mathematics (BCAM) · Bilbao, Spain
2014–16
Postdoctoral Fellow (FMJH)
École Polytechnique, CMAP · Palaiseau, France
2013–14
Postdoctoral Research Assistant
University of Bristol · Bristol, United Kingdom
QUALIFICATIONS
Selected qualifications
2025
Italian National Scientific Qualification for Full Professor in Mathematical Analysis
2020
Habilitation in Applied Mathematics / Privatdozent
TU Wien · Vienna, Austria
PAST RESEARCH INSTITUTIONS
University of Bristol
École Polytechnique
BCAM · Bilbao
TU WienFor additional professional information, consult the institutional faculty profile. Faculty portal ↗
CONNECT
Contact
For academic correspondence, research collaborations and course-related questions, you can reach me through my university contact or professional profiles.
UNIVERSITY CONTACT
Get in touch
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PROFESSIONAL PROFILES