Luis A. Caffarellis - Photo:Photo credit: Nolan Zunk / University of Texas at Austin
Photo credit: Nolan Zunk / University of Texas at Austin

Luis A. Caffarelli awarded the 2023 Abel Prize

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2023 to Luis A. Caffarelli of the University of Texas at Austin, USA, for his “seminal contributions to regularity theory for nonlinear partial differential equations includingfree-boundary problems and the Monge –Ampère equation.”

Differential equations are tools scientists use to predict the behaviour of the physical world. These equations relate one or more unknown
functions and their derivatives.The functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between
the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Partial differential equations arise naturally as laws of nature, to describe phenomena as different as the flow of water or the growth of populations. These equations have been a constant source of
intense study since the days of Isaac Newton and Gottfried Leibniz. Yet, despite substantial efforts by numerous mathematicians over centuries, fundamental questions concerning the existence, uniqueness, regularity, and stability of solutions of some of the key equations remain unresolved.

Technically virtuous results
Few other living mathematicians have contributed
more to our understanding of partial differential equations than the Argentinian–American Luis Caffarelli. He has introduced ingenious new
techniques, shown brilliant geometric insight, and produced many seminal results. Over a period of more than 40 years, he has made groundbreaking contributions to regularity theory. Regularity – or
smoothness – of solutions is essential in numerical computations, and absence of regularity is a measure of how wildly nature can behave.

“Caffarelli’s theorems have radically changed our understanding of classes of nonlinear partial differential equations with wide applications. The results are technically virtuous, covering
many different areas of mathematics and its applications,” says chair of the Abel Committee Helge Holden.

A large part of Luis A. Caffarelli’s work concerns free-boundary problems. Consider, for instance, the problem of ice melting into water. Here the free boundary is the interphase between water and ice; it is part of the unknown that is to be determined. Another example is provided by water seeping through a porous medium – again the interphase of water and the medium is to be understood.
Caffarelli has given penetrating solutions to these problems with applications to solid–liquid interphases, jet and cavitational flows, and gasand liquid flows in porous media, as well as financial mathematics.

Enormous impact on the field
Caffarelli is an exceptionally prolific mathematician,
with more than 130 collaborators and more than 30
PhD students over a period of 50 years.

“Combining brilliant geometric insight with
ingenious analytical tools and methods he has had
and continues to have an enormous impact on the
field,” says Helge Holden.

Luis A. Caffarelli has won numerous awards,
among them the Leroy P. Steele Prize for Lifetime
Achievement in Mathematics, the Wolf Prize and
the Shaw Prize.

About the Abel Prize:
The Abel Prize will be presented to Luis A.
Caffarelli at the award ceremony in Oslo on
23 May

The Abel Prize is funded by the Norwegian
government and amounts to NOK 7.5 million

The prize is awarded by the Norwegian Academy
of Science and Letters and presented by His
Majesty King Harald

The choice of the Abel laureate is based on the
recommendation by the Abel Committee, which
is composed of five internationally recognised

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