Enzo Mitidieri

Professor of Mathematical Analysis
Università degli Studi di Trieste  ·  Italy
The absence of solutions is itself a theorem — perhaps the deepest kind.
On the philosophy behind nonexistence results in nonlinear PDEs
Nonlinear PDEs Hardy–Rellich Inequalities Liouville Theory Blow-up & Nonexistence Pokhozhaev Identity Carnot Groups
01

About

Enzo Mitidieri is a professor of Mathematical Analysis at the University of Trieste. His career has produced pioneering results in the existence, nonexistence, and qualitative behavior of solutions to nonlinear PDEs, including the development — jointly with Stanislav I. Pokhozhaev (1935–2014) — of a general theory of nonexistence based on the nonlinear capacity method.

He collaborates with Victor A. Galaktionov (University of Bath) and Lorenzo D'Ambrosio (Università di Udine). He has served as Editor-in-Chief of Nonlinear Analysis A (2009–2019) and as Director of the Department of Mathematics and Informatics, University of Trieste (1997–2002). He has given invited and plenary lectures across Europe, the Americas, Russia, and Japan.

Seventeen years of joint work with Stanislav I. Pokhozhaev (1935–2014), developing a general nonexistence theory via the nonlinear capacity method.

120+
Scientific papers
46
h-index (ResearchGate)
8,131
Citations (ResearchGate)
9 · 15
PhD students · academic descendants
02

Academic Positions

1979–1983
CNR Research Fellowship — Institute of Mathematics, University of Trieste
1983–1987
Researcher (Ricercatore Universitario), Mathematical Analysis — Dept. of Mathematical Sciences, University of Trieste
1988–1991
Associate Professor of Mathematical Analysis — Dept. of Mathematics and Informatics, University of Udine
1991–1994
Associate Professor of Higher Analysis — Dept. of Mathematical Sciences, University of Trieste
1993–1994
Extraordinary Professor — University of Trieste
1994–present
Full Professor of Mathematical Analysis — University of Trieste
03

Research Themes

Liouville-type theorems & rigidity
💥
A priori estimates & blow-up
Hardy–Rellich inequalities
Δ
Higher-order elliptic systems
Nonlinear potential theory
𝔾
Sub-elliptic operators & Carnot groups
Pokhozhaev & Rellich identities
λ
Fibering method
Lane–Emden systems
CKN inequalities
Hardy–Littlewood–Sobolev systems
Riemannian manifolds
04

Books & Monographs

Pokhozhaev's Legacy: The Art of Nonexistence, Blow-up and Fibering in Nonlinear PDEs and Inequalities
V.A. Galaktionov & E. Mitidieri
to appear · 380 pages
In preparation
Liouville Theorems in Nonlinear Partial Differential Equations and Inequalities
L. D'Ambrosio & E. Mitidieri
De Gruyter Studies in Mathematics · in preparation
Under contract
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations
V.A. Galaktionov, E. Mitidieri & S.I. Pokhozhaev
Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, FL, 2015. xxvi+543 pp. ISBN: 978-1-4822-5172-2
Published 2015
A Priori Estimates and the Absence of Solutions of Nonlinear Partial Differential Equations and Inequalities
E. Mitidieri & S.I. Pokhozhaev
Tr. Mat. Inst. Steklova 234 (2001), 1–384; Proc. Steklov Inst. Math. no. 3(234), 1–362 · 9,530 download requests
Published 2001
Lecture Notes in Nonlinear Analysis: Differential Identities and Applications — Euclidean Theory, Riemannian Generalizations, and the Noether Approach to Pokhozhaev Identities
E. Mitidieri
Spring 2026 · 150 pages
Lecture Notes

Edited Volumes

1989
Semigroup Theory and Applications
Ph. Clément, S. Invernizzi, E. Mitidieri, I.I. Vrabie (eds.) · Lecture Notes in Pure and Applied Mathematics, N. 116 · M. Dekker
1991
Semigroup Theory and Evolution Equations: The 2nd International Conference
Ph. Clément, E. Mitidieri, B. de Pagter (eds.) · Lecture Notes in Pure and Applied Mathematics, N. 135 · M. Dekker
1997
Reaction Diffusion Systems
G. Caristi and E. Mitidieri (eds.) · Lecture Notes in Pure and Applied Mathematics, N. 194 · M. Dekker
1996
Special Issue dedicated to the memory of Pierre Grisvard
Ph. Clément, S. Invernizzi, E. Mitidieri (eds.) · Rend. Ist. Mat. Univ. Trieste, Vol. XXVIII (1996), 1–506
2000
Blow-up and Global Existence of Solutions for Parabolic and Hyperbolic Problems
D. Del Santo, V. Georgiev and E. Mitidieri (eds.) · Rend. Istit. Mat. Univ. Trieste 31 (2000), suppl. 2, iv+278 pp.
2009
Liouville Theorems and Detours
E. Mitidieri, E. Lanconelli and S.I. Pokhozhaev (eds.) · Nonlinear Analysis 70(8): 2825–3056
2012
Variational Analysis and Its Applications
E. Mitidieri and B.S. Mordukhovich (eds.) · Nonlinear Analysis 75(3): 983–1736
2012
In Honor of Professor V. Lakshmikantham
Sh. Ahmad, S. Carl and E. Mitidieri (eds.) · Nonlinear Analysis 75(12): 4383–4728
2013
Recent Trends in Nonlinear PDEs I: Evolution Problems
J.B. Serrin, E.L. Mitidieri, V.D. Radulescu (eds.) · Contemporary Mathematics, ~307 pp.
2013
Recent Trends in Nonlinear PDEs II: Stationary Problems
J.B. Serrin, E. Mitidieri, V.D. Radulescu (eds.) · Contemporary Mathematics, ~340 pp.
05

Selected Publications

2025
Liouville theorems of semilinear elliptic inequalities in a half-space
with L. D'Ambrosio
2025
Characterization of positive superharmonic functions in a half-space
with L. D'Ambrosio
Calculus of Variations and PDE, in press (2026), 1–41
2024
A view on Liouville Theorems in PDEs
E. Mitidieri — dedicated to E. Lanconelli on his 80th birthday
Analysis and Geometry in Metric Spaces 12(1) (2024), 20240008
2000
A simple approach to Hardy inequalities
E. Mitidieri
Math. Notes 67 (2000), 479–486
1993
A Rellich type identity and applications
E. Mitidieri
Commun. in Partial Differential Equations 18(1–2) (1993), 125–151
→ Full list of publications (120+ papers)  ·  MathSciNet · Google Scholar · zbMATH
06

Invited Research Talks (selected)

2015 — PlenaryNonlinear Phenomena in Mathematics and Economics (tribute to John Forbes Nash), RISM Varese
2005 — PlenaryFunction Spaces, Approximation Theory, Nonlinear Analysis, Moscow (100th birthday of Acad. S.M. Nikol'skii)
2025XIII Brazilian-Italian Workshop in Nonlinear Differential Equations, Modena
2024Two Nonlinear Days in Urbino, Università di Urbino Carlo Bo
2023RISM Workshop "Analysis and PDEs" (Radulescu 65th birthday), Varese
2018Recent Advances in Nonlinear Analysis (Radulescu 60th birthday), Levico Terme
2018Two Nonlinear Days in Urbino

Visiting Professorships

1982University of Tennessee, Knoxville (USA)
1986University of Delft (Netherlands)
1988UNICAMP, Campinas (Brazil)
1990Universidad Autónoma de Madrid (Spain)
1992Universiteit Leiden (Netherlands)
1993UNICAMP (Brazil)
1993Universidad de Chile, Santiago
1995University of Helsinki (Finland)
1995Universiteit Delft (Netherlands)
1996UNICAMP (Brazil)
1998Université Toulouse III (France)
1998University of Houston (USA)
2001Steklov Mathematical Institute, Moscow
2005Steklov Mathematical Institute, Moscow
07

Conference Organisation

1985 — Variational Methods in Differential Problems, Trieste
1987 — Trends in Semigroup Theory and Applications, Trieste
1989 — Semigroup Theory and Evolution Equations – 2nd International Conference, Delft (Netherlands)
1995 — Reaction Diffusion Systems, Trieste, 2–7 October 1995
1998–2000 — Matematica 2000, Università di Trieste
1999 — Blow-up and Global Existence of Solutions of Nonlinear Parabolic and Hyperbolic Problems, University of Trieste, 27–29 September 1999
2001 — Linear and Nonlinear Hyperbolic Equations (with F. Colombini and D. Del Santo), Grado
2008 — Liouville Theorems and Detours, INdAM Conference, Cortona, 18–24 May 2008
08

Teaching Activity

Undergraduate Courses

A.A. 1980/81–1992/93 — Analisi Matematica I, II, Analisi Superiore, Analisi Funzionale, Analisi Reale (Univ. Trieste)
A.A. 1988/89 — Analisi Superiore (Univ. Trieste); Analisi Matematica II (Univ. Udine)
A.A. 1990/91 — Analisi Matematica II (Univ. Udine)
A.A. 1991/92 — Analisi Matematica II (Univ. Udine); Analisi Superiore (Univ. Trieste)
A.A. 1992/93–2022/23 — Analisi Matematica I, II, Analisi Superiore, Analisi Funzionale, Analisi Reale, Analisi di Fourier, Istituzioni di Analisi Superiore II, Equazioni differenziali, Metodi matematici per l'ingegneria (Univ. Trieste)

Doctoral Teaching

A.A. 1993/94 — Maximum principles for elliptic systems (SISSA)
A.A. 1999/2000 — Stime a priori per soluzioni di equazioni e sistemi ellittici (SISSA)
A.A. 2000/2001 — Teoremi di non esistenza e applicazioni alla teoria delle equazioni alle derivate parziali (Università di Pisa)
Special seminars at SISSA and ICTP on: evolution equations associated to monotone operators; sum of maximal monotone operators; periodic solutions of the semilinear wave equation (Brezis–Coron theorems); Volterra integral equations in Hilbert spaces; existence and asymptotic behaviour of solutions to Volterra equations in infinite-dimensional spaces
09

Doctoral Students

9 students · 15 academic descendants · Mathematics Genealogy Project

PhD Supervised

Lorenzo D'Ambrosio
SISSA, Trieste
23 October 2002
Hardy Inequalities and Liouville Type Theorems Associated to Degenerate Operators
Fabio Pezzolo
University of Trieste
25 March 2022
On Some Multilinear Type Integral Systems

Undergraduate Students Supervised

Ramon Soranzo
Università di Trieste
1989
Massimo Iengo
Università di Trieste
1995
Omar Lakkis
Università di Trieste
1996
Sandro Curzola
Università di Trieste
1997
Atanasio Pantarrotas
Università di Trieste
1997
Caterina Cusulin
Università di Trieste
2001
Anna Dall'Acqua
Università di Trieste
2001
Sara Noviello
Università di Trieste
2003
Valentina Sanabor
Università di Trieste
2005
Giulia Elena Bozzao
Università di Trieste
2023
10

Editorial Roles

2026–
Journal of Mathematical Sciences
Associate Editor
2009–2019
Nonlinear Analysis A: Theory, Methods and Applications
Editor-in-Chief
2019–
Nonlinear Analysis: Theory, Methods and Applications
Honorary member of the Editorial Board
2006–2009
Nonlinear Analysis A: Theory, Methods and Applications
Associate Editor
2006–2012
Nonlinear Analysis B: Real World Applications
Associate Editor
2000–2002
Abstract and Applied Analysis
Associate Editor
2010–2011
ISRN Mathematical Analysis
Associate Editor
2013–
Honorary member of the Editorial Board

Referee Activity (selected journals)

Administrative Roles

1997–2002
Director, Department of Mathematics and Informatics, University of Trieste
2021–2024
Member, Research Evaluation Committee (CVR), University of Trieste
PhD Committee
PHD09 – Scienze della Terra, Fluidodinamica e Matematica, XXXIII–XXXV Ciclo
International
Representative of the Boards of Deans on the Promotion PhD Committee, University of Delft, The Netherlands
11

Metrics & Online Profiles

108
Indexed publications
MathSciNet
4,374
Total citations
MathSciNet (in 2,526 papers)
1,982
Unique citing authors
MathSciNet
46
h-index
ResearchGate
8,131
Citations
ResearchGate
40,796
Reads
ResearchGate
141
Recommendations
ResearchGate
4,701
Research Interest Score
ResearchGate
9,530
Downloads of Steklov 2001
mathnet.ru
Online profiles: Top Italian Scientists · Research.com · AD Scientific Index · ORCID 0000-0001-5042-9401 · ResearchGate — Publications · Semantic Scholar · MathSciNet · Rankless · UniTS — MIGE
12

Web Sites

🏛️ UniTS — MIGE 🌐 enzomitidieri.xyz 🔬 Semantic Scholar
13

Contact

Address

Dipartimento di Matematica e Geoscienze
Università degli Studi di Trieste
Via Weiss 2, 34128 Trieste, Italy

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