Appl Math Optim 46:79–80 (2002)
2002 Springer-Verlag New York Inc.
Jacques-Louis Lions passed away on May 17, 2001 at the age of 73. He was a founder,
in 1972, of Applied Mathematics & Optimization, along with A.V. Balakrishnan,
G.I. Marchuk, and L.S. Pontryagin. He had also a profound inﬂuence in the mathe-
matics related to science, more speciﬁcally, in the general area of Partial Differential
Equations (PDE), their numerical analysis, their control theoretic properties, etc., both
at the deterministic and stochastic levels.
In dedicating this special issue to him, AMO wishes to pay tribute to his memory
and to the lasting legacy of his work. This issue gathers invited papers, authored or
co-authored by prominent mathematicians, who had a professional and/or personal
association with J.L. Lions and AMO.
Several lengthy obituaries have already appeared in print since his death. In partic-
ular, we would like to cite the obituary dedicated to him in the Notices of the American
Mathematical Society, Volume 48, Number 11, pp. 1315–1321. Here it would be appro-
priate just to provide a brief summary of his impressive multifaceted work.
The scientiﬁc work of J.L. Lions is vast and encompasses many areas under a uni-
fying theme, which is the study of PDE in many of its aspects: from abstract theory to
numerical schemes; from control theory to modeling; from deterministic to stochastic
analysis. It includes, but is not limited to, the following areas: variational inequalities
for elliptic and evolution equations (around 1950–54); strongly nonlinear equations that
are monotone in the highest argument (around 1965); interpolation theory and Sobolev
spaces in themselves as well as in the study of nonhomogeneous boundary value problems
(late 1960s); continuum mechanics and physics (around 1972); numerical analysis of
PDE and variational inequalities; quasi-variational inequalities in stochastic control and
impulse control; control theory of PDE (since 1968); domain decomposition in numerical
analysis (since 1972); homogenization (late 1970s–1980s) employing PDE, asymptotic
and stochastic analysis; G- and Gamma-convergence (in the 1980s); mathematical me-
teorology (in the late 1990s) to include modeling of primitive equations governing the
motion of the atmosphere, the ocean, and their coupling and related asymptotics and
numerical issues, etc.
J.L. Lions authored or co-authored about 20 books and almost 600 articles. He
is widely regarded as the founder of the French School of applied mathematics, with
widespread ties to many mathematical communities in various countries across the world.