Enzo Mitidieri

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

h-index (ResearchGate)

8,090

Citations (ResearchGate)

9 · 15

PhD students · academic descendants

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

Books & Monographs

Pokhozhaev's Legacy: The Art of Nonexistence, Blow-up and Fibering in Nonlinear PDEs and Inequalities

E. Mitidieri & V.A. Galaktionov

to appear · 380 pages

In preparation

Liouville Theorems in Nonlinear Partial Differential Equations and Inequalities

E. Mitidieri & L. D'Ambrosio

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 · 140 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. Pohozhaev (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.

Selected Publications

2025

Liouville theorems of semilinear elliptic inequalities in a half-space

with L. D'Ambrosio

Journal of Differential Equations 447 (2025), 113664

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

2022

Entire solutions of certain fourth order elliptic problems and related inequalities

with L. D'Ambrosio

Advances in Nonlinear Analysis 11 (2022), no. 1, 785–829

2020

On some multicomponent quasilinear elliptic systems

with L. D'Ambrosio

J. Math. Anal. Appl. 490 (2020), no. 1, 124207

2019

Representation formulae of solutions of second order elliptic inequalities

with L. D'Ambrosio

Nonlinear Analysis 178 (2019), 310–336

2018

Quasilinear elliptic systems in divergence form associated to general nonlinearities

with L. D'Ambrosio

Advances in Nonlinear Analysis 7 (2018), no. 4, 425–447

2017

Quasilinear elliptic equations with critical potentials

with L. D'Ambrosio

Advances in Nonlinear Analysis 6 (2017), no. 2, 147–164

2015

Uniqueness of solutions of a class of quasilinear subelliptic equations

with L. D'Ambrosio

Geometric Methods in PDE's, Springer INdAM Series 13, 177–198 (2015)

2014

Classification of global and blow-up sign-changing solutions of a semilinear heat equation in the subcritical Fujita range

with V.A. Galaktionov and S.I. Pokhozhaev

Advanced Nonlinear Studies 14 (2014), 1–31

2014

Hardy–Littlewood–Sobolev systems and related Liouville theorems

with L. D'Ambrosio

Discrete and Continuous Dynamical Systems – Series S 7, No. 4 (2014), 653–671

2013

Comparison principle, uniqueness and symmetry of entire solutions of quasilinear elliptic equations

L. D'Ambrosio, A. Farina, E. Mitidieri and J. Serrin

Nonlinear Analysis 90 (2013), 135–158

2013

Entire solutions of quasilinear elliptic systems on Carnot groups

with L. D'Ambrosio

Proceedings of the Steklov Institute of Mathematics 283 (2013), 3–19

2012

A priori estimates and reduction principles for quasilinear elliptic problems

with L. D'Ambrosio

Advances in Differential Equations 17, Nos. 9–10 (2012), 935–1000

2010

A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities

with L. D'Ambrosio

Advances in Mathematics 224, Issue 3 (2010), 967–1020

2006

Representation formulae and inequalities for solutions of second order PDEs

with L. D'Ambrosio and S.I. Pokhozhaev

Trans. Amer. Math. Soc. 358 (2006), 893–910

2004

Hardy inequalities with optimal constants and remainder terms

with F. Gazzola and H.-Ch. Grunau

Trans. Amer. Math. Soc. 356, No. 6 (2004), 2149–2168

2003

Existence of Multiple Solutions for Quasilinear Systems via Fibering Method

with Yu. Bozhkov

Journal of Differential Equations 190, No. 1 (2003), 239–267

2000

A simple approach to Hardy inequalities

E. Mitidieri

Math. Notes 67 (2000), 479–486

1998

Strongly indefinite systems with critical Sobolev exponents

with J. Hulshof and R.C.A.M. van der Vorst

Trans. Amer. Math. Soc. 350 (1998), 2349–2365

1998

Liouville Theorems for Elliptic Inequalities and Applications

with I. Birindelli

Proc. Royal Society of Edinburgh 128A (1998), 1217–1247

1993

A Rellich type identity and applications

E. Mitidieri

Commun. in Partial Differential Equations 18(1–2) (1993), 125–151

1993

Positive solutions for a quasilinear system via blow-up

with Ph. Clément and R. Manasevich

Comm. PDE 18 (1993), 2071–2106

1986

A maximum principle for an elliptic system and application to semilinear problems

E. Mitidieri

SIAM J. Math. Anal. 17 (1986), 836–849

Complete list (120+ papers): MathSciNet · Google Scholar · zbMATH

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

2017James Serrin: From His Legacy to the New Frontiers, Perugia

2016INdAM Workshop Geometric Properties for Parabolic and Elliptic PDEs (2nd Italian-Japanese Workshop), Cortona

2016Liouville Theorems in PDEs: Old and New, Seminario Matematico e Fisico di Milano

2014Liouville Theorems Old and New, Martin-Luther-Universität Halle-Wittenberg

2012Workshop in Honor of Patrizia Pucci's 60th Birthday, Perugia

2010Second Meeting of the Women of the Laplacian, Monopoli

2008Geometric Methods in PDEs (65th birthday of E. Lanconelli), Bologna

2008Liouville Theorems and Detours, INdAM Conference, Cortona

2008Conferenze di Analisi Matematica, Omaggio a Calogero Vinti, Perugia

2008International Workshop on PDE for the 80th birthday of James Serrin, Perugia

2006Liouville Theorems in Riemannian and Sub-Riemannian Settings, University of Bologna

2005Harnack Inequalities and Positivity for PDE, Cortona

2002Symposium on PDE in celebration of James Serrin's 75th birthday, Perugia

2001Function Spaces, Approximation Theory, Steklov Mathematical Institute, Moscow

2000Functional Analysis and PDE, Oberwolfach

2000Partial Differential Equations and Related Topics, Università di Pisa

1998Third School on Nonlinear Functional Analysis, ICTP Trieste

1998The Delft Meeting on Functional Analysis and Nonlinear PDEs

1996Fifth International Conference on Evolution Equations, Hiroshima

1995Analysis Year in Finland, Helsinki

1993Symmetry and Asymptotics for Nonlinear Systems, Ohio University

1993Conference on Schrödinger Operators, Erwin Schrödinger Institute, Vienna

1992World Congress of Nonlinear Analysis, Tampa (USA)

1989Oberwolfach Meeting (H. Amann and P. Hess)

1988College on Variational Problems in Analysis, ICTP Trieste

1985Nonlinear Variational Problems, Isola d'Elba – Lacona

1982Dept. of Mathematics, University at Buffalo (New York)

1982Vanderbilt University, Nashville

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

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

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

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

1997–2003

Rendiconti dell'Istituto Matematico dell'Università di Trieste

Editor-in-Chief

2013–

Rendiconti dell'Istituto Matematico dell'Università di Trieste

Honorary member of the Editorial Board

Referee Activity (selected journals)

Annali della Scuola Normale Superiore di Pisa Bollettino della Unione Matematica Italiana Journal of Mathematical Analysis and Applications Journal of Differential Equations Advances in Differential Equations Advances in Nonlinear Analysis Mathematische Annalen Transactions of the American Mathematical Society Rocky Mountain Journal of Mathematics Differential and Integral Equations SIAM Journal on Mathematical Analysis Journal of Functional Analysis Annales Academiae Scientiarum Fennicae, Mathematica Communications in Partial Differential Equations Proceedings of the Royal Society of Edinburgh Mathematische Zeitschrift Bulletin of the Belgian Mathematical Society Proceedings of the American Mathematical Society Advanced Nonlinear Studies Annales de l'Institut Henri Poincaré Mathematical Methods in the Applied Sciences Nonlinear Analysis: Theory, Methods and Applications Nonlinear Analysis: Real World Applications Quarterly of Applied Mathematics Proceedings of the Steklov Mathematical Institute Advances in Mathematics Communications in Pure and Applied Mathematics Journal d'Analyse Mathématique

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

About

Academic Positions

Research Themes

Books & Monographs

Edited Volumes

Selected Publications

Invited Research Talks (selected)

Visiting Professorships

Conference Organisation

Teaching Activity

Undergraduate Courses

Doctoral Teaching

Doctoral Students

PhD Supervised

Undergraduate Students Supervised

Editorial Roles

Referee Activity (selected journals)

Administrative Roles

Metrics & Online Profiles

Contact

Email

Address

Academic Profiles

Institution