mathematics

Giuseppe Mingione

Giuseppe Mingione 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 Giuseppe Mingione rather than just read about it. In short: Giuseppe Mingione (born 28 August 1972) is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations. Scientific activity Mingione received his Ph.D. in mathematics from the University of Naples Federico II in 1999 having Nicola Fusco as advisor; he is professor of mathematics at the University of Parma.

Key takeaways

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

Reference excerpt

Giuseppe Mingione (born 28 August 1972) is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations.

Scientific activity Mingione received his Ph.D. in mathematics from the University of Naples Federico II in 1999 having Nicola Fusco as advisor; he is professor of mathematics at the University of Parma. He has mainly worked on regularity aspects of the Calculus of Variations, solving a few longstanding questions about the Hausdorff dimension of the singular sets of minimisers of vectorial integral functionals and the boundary singularities of solutions to nonlinear elliptic systems. This connects to the work of authors as Almgren, De Giorgi, Morrey, Giusti, who proved theorems asserting regularity of solutions outside a singular set (i.e. a closed subset of null measure) both in geometric measure theory and for variational systems of partial differential equations. These are indeed called partial regularity results and one of the main issues is to establish whether the dimension of the singular set is strictly less than the ambient dimension. This question found a positive answer for general integral functionals, thanks to the work of Kristensen and Mingione, who also gave explicit estimates for the dimension of the singular sets of minimisers. Mingione also worked on nonlinear potential theory obtaining potential estimates for solutions to nonlinear elliptic and parabolic equations. Such estimates allow to give a unified approach to the regularity theory of quasilinear, degenerate equations and relate to and upgrade previous work of Kilpeläinen, Malý, Trudinger, Wang. Together with Cristiana De Filippis, Mingione proved a Schauder type theory for nonuniformly elliptic equations and functionals.

Recognition Mingione was awarded the 2005 Bartolozzi Prize, the 2006 Stampacchia Medal, the 2010 Caccioppoli Prize and the 2016 Amerio Prize. In 2007 he was awarded an ERC grant. Mingione is listed as an ISI highly cited researcher and was invited to deliver the ETH Zürich Nachdiplom Lectures in 2015..He was invited speaker at the 2016 European Congress of Mathematics in Berlin. In 2017 he was appointed Commander of the Order of Merit of the Italian Republic by the President of the Italian Republic.

References

External links Website Site of Caccioppoli Prize Archived 2018-10-11 at the Wayback Machine Site of European Research Council

Illustrations

Worked examples

Example 1 — a first encounter with Giuseppe Mingione

Start with the simplest possible case. Write down what Giuseppe Mingione 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 Giuseppe Mingione 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 Giuseppe Mingione 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 Giuseppe Mingione

In research: Giuseppe Mingione 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 Giuseppe Mingione 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: Giuseppe Mingione is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1972 births, 21st-century Italian mathematicians, Academic staff of the University of Parma, so understanding it makes those chapters shorter.
In everyday life: Look for Giuseppe Mingione 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 Giuseppe Mingione in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Giuseppe Mingione 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 Giuseppe Mingione out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Giuseppe Mingione in simple terms?

Giuseppe Mingione (born 28 August 1972) is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations. Scientific activity Mingione received his Ph.D. in mathematics from the University of Naples Federico II in 1999 having Nicola Fusco as advis…

Why does Giuseppe Mingione 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 Giuseppe Mingione?

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 Giuseppe Mingione.