mathematics

Luis Caffarelli

Luis Caffarelli 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 Luis Caffarelli rather than just read about it. In short: Luis Ángel Caffarelli (Spanish pronunciation: [ˈlwis 'anxel kafaˈɾeli]; born December 8, 1948) is an Argentine-American mathematician. He studies partial differential equations and their applications.

Key takeaways

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

Reference excerpt

Luis Ángel Caffarelli (Spanish pronunciation: [ˈlwis 'anxel kafaˈɾeli]; born December 8, 1948) is an Argentine-American mathematician. He studies partial differential equations and their applications. Caffarelli is a professor of mathematics at the University of Texas at Austin, and the winner of the 2023 Abel Prize.

Career Caffarelli was born and grew up in Buenos Aires. He obtained his Masters of Science (1968) and Ph.D. (1972) at the University of Buenos Aires. His Ph.D. advisor was Calixto Calderón. He currently holds the Sid Richardson Chair at the University of Texas at Austin and is core faculty at the Oden Institute for Computational Engineering and Sciences. He also has been a professor at the University of Minnesota, the University of Chicago, and the Courant Institute of Mathematical Sciences at New York University. From 1986 to 1996 he was a professor at the Institute for Advanced Study in Princeton.

Research Caffarelli published "The regularity of free boundaries in higher dimensions" in 1977 in Acta Mathematica. One of his most cited results regards the Partial regularity of suitable weak solutions of the Navier–Stokes equations; it was obtained in 1982 in collaboration with Louis Nirenberg and Robert V. Kohn.

Awards and recognition In 1991, he was elected to the U.S. National Academy of Sciences. He was awarded honorary doctorates by the École Normale Supérieure, Paris, the University of Notre Dame, the Universidad Autónoma de Madrid, and the Universidad de La Plata, Argentina. He received the Bôcher Memorial Prize in 1984. He is listed as an ISI highly cited researcher. In 2003, Konex Foundation from Argentina granted him the Diamond Konex Award, one of the most prestigious awards in Argentina, as the most important Scientist of his country in the last decade. In 2005, he received the prestigious Rolf Schock Prize of the Royal Swedish Academy of Sciences "for his important contributions to the theory of nonlinear partial differential equations". He also received the Leroy P. Steele Prize for Lifetime Achievement in Mathematics in 2009. In 2012, he was awarded the Wolf Prize in Mathematics (jointly with Michael Aschbacher) and became a fellow of the American Mathematical Society. In 2017 he gave the Łojasiewicz Lecture (on "Some models of segregation") at the Jagiellonian University in Kraków. In 2018, he was named a SIAM Fellow and he received the Shaw Prize in Mathematics. In 2023, he was awarded the Abel Prize "for his seminal contributions to regularity theory for nonlinear partial differential equations including free-boundary problems and the Monge–Ampère equation".

Bibliography Caffarelli has coauthored two books:

Fully Nonlinear Elliptic Equations by Luis Caffarelli and Xavier Cabré (1995), American Mathematical Society. ISBN 0-8218-0437-5 A Geometric Approach to Free Boundary Problems by Luis Caffarelli and Sandro Salsa (2005), American Mathematical Society. ISBN 0-8218-3784-2

References

External links Luis Caffarelli at the Mathematics Genealogy Project Home page Biographical data

Illustrations

Worked examples

Example 1 — a first encounter with Luis Caffarelli

Start with the simplest possible case. Write down what Luis Caffarelli 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 Luis Caffarelli 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 Luis Caffarelli 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 Luis Caffarelli

In research: Luis Caffarelli 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 Luis Caffarelli 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: Luis Caffarelli is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1948 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Luis Caffarelli 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 Luis Caffarelli in 20 minutes

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

Frequently asked questions

What is Luis Caffarelli in simple terms?

Why does Luis Caffarelli 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 Luis Caffarelli?

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 Luis Caffarelli.