mathematics

Paolo Marcellini

Paolo Marcellini is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Paolo Marcellini rather than just read about it. In short: Paolo Marcellini (born 25 June 1947 in Fabriano) is an Italian mathematician who deals with mathematical analysis. He was a full professor at the University of Florence,as of now he is a "Professor Emeritus", working on partial differential equations, calculus of variations and related mathematics.

Key takeaways

Paolo Marcellini belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Paolo Marcellini to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Paolo Marcellini from memory before moving on to harder problems.

Reference excerpt

Paolo Marcellini (born 25 June 1947 in Fabriano) is an Italian mathematician who deals with mathematical analysis. He was a full professor at the University of Florence,as of now he is a "Professor Emeritus", working on partial differential equations, calculus of variations and related mathematics. He was the Director of the Italian National Group GNAMPA of the Istituto Nazionale di Alta Matematica (INdAM) and Dean of the Faculty of Mathematical, Physical and Natural Sciences of the University of Florence.

Biography Marcellini received his Laurea Degree in 1971 at the Sapienza University of Rome and made his postgraduate studies from 1971–1973 at the Scuola Normale Superiore in Pisa under the supervision of Ennio De Giorgi. After that he was assistant and finally a lecturer at the University of Florence, in 1981 full professor at the University of Naples and then at the University of Tor Vergata in Rome. Since 1985 he is Professor of Analysis in Florence. He was there Dean of the Faculty of Mathematics, Physics and Natural Sciences, Director of the Department of Mathematics "Ulisse Dini" and Coordinator of the graduate program in mathematics (PhD Doctoral Studies). He was a visiting scientist, among others, the Collège de France in Paris, Bonn and Leipzig (University and Max Planck Institute), University of California at Berkeley, EPFL at Lausanne, Mathematical Institute of the University of Oxford, Carnegie-Mellon University in Pittsburgh, Lisbon, Instituto Argentino de Matematica in Buenos Aires, Russian Academy of Sciences Akademgorodok in Novosibirsk, the Institute for Advanced Study in Princeton, the University of Texas at Austin, University of Zurich, University of Cologne in Köln, University of Erlangen-Nuremberg, Hokkaido University in Tokyo, Academia Sinica in Taipei-Taiwan, the Australian National University and the Mittag-Leffler Institute in Sweden. His academic interests mostly lie in the fields of calculus of variations and partial differential equations, including applications, for example in the theory of non-linear elasticity and in biology. From 1999 to 2003 he was in Scientific Direction of the Istituto Nazionale di Alta Matematica in Rome. In 2007 he became a member of Academy of Sciences of the Tuscany "La Colombaria". From 2013 to 2017 he has been the elected Director of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

Recognition In August 2023 Paolo Marcellini was selected as the winner of the 2022 Ames JMAA Prize, awarded annually for the best paper published in the Journal of Mathematical Analysis and Applications (JMAA) in the last three years. His paper “Growth conditions and regularity for weak solutions to nonlinear elliptic pdes”, JMAA, 501 (September 2021), 124408, was chosen unanimously by the Committee chaired by Professor José Bonet Solves. The award consists of a certificate of merit and a monetary prize donated by Elsevier and the American Mathematical Society (AMS).

Bibliography with Bernard Dacorogna: Implicit partial differential equations, Birkhäuser 1999. with Bernard Dacorogna, Emanuele Paolini: Origami and Partial Differential Equations, Notices of the AMS, 57, May 2010, 598, Online with Carlo Sbordone: Analisi Matematica Uno, Napoli: Liguori 1996. with Carlo Sbordone, Nicola Fusco: Analisi Matematica Due, Napoli: Liguori 1996. with Carlo Sbordone, Nicola Fusco: Mathematical Analysis, Functions of Several Real Variables and Applications, Springer, January 2023, ISBN 978-3-031-04150-1.

Selected publications Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals, Manuscripta Math., 51, 1985, pp. 1–28. Regularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions, Arch. Rational Mech. Anal., 105, 1989, 267–284. Regularity and existence of solutions of elliptic equations with p,q-growth conditions, J. Differential Equations, 90, 1991, 1–30. with Bernard Dacorogna: General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acta Mathematica, 178, 1997, 1–37. with Irene Fonseca, Nicola Fusco: On the total variation of the Jacobian, J. Funct. Anal., 207, 2004, 1–32. with Bernard Dacorogna, Emanuele Paolini: Origami and Partial Differential Equations, Notices of the AMS, 57, May 2010, 598, Online with Verena Bögelein, Frank Duzaar: Parabolic Systems with p,q-Growth: A Variational Approach, Arch. Ration. Mech. Anal., 210, 2013, 219–267. with Verena Bögelein, Frank Duzaar: Existence of evolutionary variational solutions via the calculus of variations, J. Differential Equations, 256, 2014, 3912–3942. Growth conditions and regularity for weak solutions to nonlinear elliptic pdes, Journal of Mathematical Analysis and Applications, 501, 2021, 124408 / Online

External links Paolo Marcellini at the Mathematics Genealogy Project / PM Homepage Gnampa - Gnampa-INdAM / PM on Scopus - on Scopus / PM on Google Scholar - on Google Scholar / Ames Prize - 2022 Ames JMAA Prize by Elsevier / Ames Prize - 2022 Ames JMAA Prize by American Mathematical Society (AMS)

Illustrations

Worked examples

Example 1 — a first encounter with Paolo Marcellini

Start with the simplest possible case. Write down what Paolo Marcellini claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Paolo Marcellini before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Paolo Marcellini ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Paolo Marcellini

In research: Paolo Marcellini appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Paolo Marcellini in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Paolo Marcellini is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1947 births, 20th-century Italian mathematicians, 21st-century Italian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paolo Marcellini outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Paolo Marcellini in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Paolo Marcellini means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Paolo Marcellini out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Paolo Marcellini in simple terms?

Why does Paolo Marcellini matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Paolo Marcellini?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Paolo Marcellini.