mathematics

Mariano Giaquinta

Mariano Giaquinta 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 Mariano Giaquinta rather than just read about it. In short: Mariano Giaquinta (born Caltagirone, 1947), is an Italian mathematician mainly known for his contributions to the fields of calculus of variations and regularity theory of partial differential equation. He is currently professor of Mathematics at the Scuola Normale Superiore di Pisa and he is the director of De Giorgi center at Pisa.

Key takeaways

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Reference excerpt

Mariano Giaquinta (born Caltagirone, 1947), is an Italian mathematician mainly known for his contributions to the fields of calculus of variations and regularity theory of partial differential equation. He is currently professor of Mathematics at the Scuola Normale Superiore di Pisa and he is the director of De Giorgi center at Pisa.

Career Giaquinta is well known for his basic work in elliptic regularity theory, and especially in the setting of vectorial variational problems. Together with Enrico Giusti he has obtained innovative results on the regularity of minima of variational integrals and related singular sets. The main novelty is in the fact that, for the first time, the regularity of minimizers is obtained using directly the minimality properties without appealing to Euler–Lagrange equation of the functionals, which in general is not supposed to exist in the cases considered. His work with Giuseppe Modica on the local higher integrability properties of solutions to elliptic systems has had an influence on the development of partial regularity theory. Many of these results are summarized in his 1983 book. Giaquinta has been one of the founders, and for many years the managing editor, of the journal "Calculus of Variations and PDE".

Awards Giaquinta won the Bartolozzi Prize of the Italian Mathematical Union in 1979, in 1990 he was awarded with Humboldt research award and in 2006 with the Amerio Prize. He has been an invited speaker at the 1986 International congress of mathematicians. Giaquinta belongs to the ISI list of highly cited researchers in Mathematics and he is a member of the German Academy of Sciences.

Selected publications Giaquinta, Mariano (1983), Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies, vol. 105, Princeton, New Jersey: Princeton University Press, pp. vii+297, ISBN 0-691-08330-4, MR 0717034, Zbl 0516.49003. Giaquinta, Mariano; Hildebrandt, Stefan (1996), Calculus of Variations I. The Lagrangian Formalism, Grundlehren der Mathematischen Wissenschaften, vol. 310 (1st ed.), Berlin: Springer–Verlag, pp. xxix+475, ISBN 3-540-50625-X, MR 1368401, Zbl 0853.49001. Giaquinta, Mariano; Hildebrandt, Stefan (1996), Calculus of Variations II. The Hamiltonian Formalism, Grundlehren der Mathematischen Wissenschaften, vol. 311 (1st ed.), Berlin: Springer–Verlag, pp. xxx+652, ISBN 3-540-57961-3, MR 1385926, Zbl 0853.49002. Giaquinta, Mariano; Modica, Giuseppe; Souček, Jiří (1998), Cartesian Currents in the Calculus of Variation I. Cartesian Currents, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 37, Berlin-Heidelberg-New York: Springer Verlag, pp. xxiv+711, ISBN 3-540-64009-6, MR 1645086, Zbl 0914.49001. Giaquinta, Mariano; Modica, Giuseppe; Souček, Jiří (1998), Cartesian Currents in the Calculus of Variation II. Variational integrals, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 38, Berlin-Heidelberg-New York: Springer Verlag, pp. xxiv+697, ISBN 3-540-64010-X, MR 1645082, Zbl 0914.49002.

References

Worked examples

Example 1 — a first encounter with Mariano Giaquinta

Start with the simplest possible case. Write down what Mariano Giaquinta 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 Mariano Giaquinta 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 Mariano Giaquinta 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 Mariano Giaquinta

In research: Mariano Giaquinta 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 Mariano Giaquinta 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: Mariano Giaquinta is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1947 births, 21st-century Italian mathematicians, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Mariano Giaquinta 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 Mariano Giaquinta in 20 minutes

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Close the page and write down what Mariano Giaquinta means in your own words.
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Frequently asked questions

What is Mariano Giaquinta in simple terms?

Why does Mariano Giaquinta 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 Mariano Giaquinta?

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 Mariano Giaquinta.