Jacques-Louis Lions Research Articles

Computer-aided medicine and surgery

Marc Thiriet' was educated at Medicine Faculty of Lille and University Pierre and Marie Curie ([UPMC] MD), and then at Technology University of Compiègne (3 rd cycle Doctorate in Biomechanics), and Physics College of University Denis Diderot (Accreditation to Supervise Research). He was assistant physician in the lung disease department of Pontoise hospital. He is currently a member of the INRIA-UPMC-CNRS team REO in Laboratory Jacques-Louis Lions (applied math.) of UPMC. He worked in flows in collapsible tubes applied to airways and veins, 3D unsteady developing laminar flows in bend and branchings, both experimentally and numerically, as well as in models derived from 3D reconstruction of human anatomy. He is now involved in mathematical modeling of biological processes. Marc Thiriet is the author of Biology and Mechanics of Blood Flows (2˜Vols.) and the book series “Biomathematical and Biomechanical Modeling of the Circulatory and Ventilatory Systems'' (7˜published books). He was the associate editor for the medical encyclopedia “Pan Vascular Medicine”. He also wrote the chapter 30. Biofluid Flow and Heat Transfer of Handbook of Fluid Dynamics. He is the President of the French Committee for Intensive Computation in Biology and Medicine.

On a lemma of Jacques-Louis Lions and its relation to other fundamental results

Let Ω be a domain in RN, i.e., a bounded and connected open subset of RN with a Lipschitz-continuous boundary ∂Ω, the set Ω being locally on the same side of ∂Ω. A fundamental lemma, due to Jacques-Louis Lions, provides a characterization of the space L2(Ω), as the space of all distributions on Ω whose gradient is in the space H−1(Ω). This lemma, which provides in particular a short proof of a crucial inequality due to J. Nečas, is also a key for proving other basic results, such as, among others, the surjectivity of the divergence operator acting from H01(Ω) into L02(Ω), a “weak” form of the Poincaré lemma or a “simplified version” of de Rham theorem, each of which provides sufficient conditions insuring that a vector field in H−1(Ω) is the gradient of a function in L2(Ω). The main objective of this paper is to establish an “equivalence theorem”, which asserts that J.L. Lions lemma is in effect equivalent to a number of other fundamental properties, which include in particular the ones mentioned above. The key for proving this theorem is a specific “approximation lemma”, itself one of these equivalent results, which appears to be new to the best of our knowledge. Some of these equivalent properties can be given an independent, i.e., “direct”, proof, such as for instance the constructive proof by M.E. Bogovskii of the surjectivity of the divergence operator. Therefore, the proof of any one of such properties provides, by way of our equivalence theorem, a means of proving J.L. Lions lemma, the known “direct” proofs of which for a general domain are notoriously difficult.

Remarks on a lemma by Jacques-Louis Lions

Let Ω be a bounded and connected open subset of RN with a Lipschitz-continuous boundary ∂Ω, the set Ω being locally on one side of ∂Ω. It is shown in this Note that a fundamental characterization of the space L2(Ω) due to Jacques-Louis Lions is in effect equivalent to a variety of other properties. One of the keys for establishing these equivalences is a specific “approximation lemma”, itself one of these equivalent properties.

About two types of microstructures adapted to heat evacuation and elastic stress: snow flakes and quasi-crystals

I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor (Jacques-Louis LIONS) could not come, and he had proposed my name. I was happily surprised that Constantine greeted me as if he knew me well, and since for many years now I have considered him as if he was an older brother, I wonder when this feeling started. I do not remember when I told him that my paternal grandmother (Cecilia) had a Greek passport, which was not uncommon for Christian families in Syria, since most of them followed the Greek Orthodox rite, and I now wonder if it played a role in the divorce of my grandparents, after my grandfather (Elias) switched to a more evangelical faith, and became a little excessive about religion: my father (Georges) once mentioned that when he had some argument with his father and he wanted to annoy him, he went to the Sunday office at the Greek Orthodox church. Becoming friend with Constantine was natural for human reasons, but also for scientific reasons.

Foreword

Professor Ta-Tsien Li was born on November 10, 1937, in Nantong,Jiangsu Province, China. He was graduated in 1957 from theDepartment of Mathematics, Fudan University, and has been itsfaculty member since then. His in-service graduate study as astudent of Professor Chao-Hao Gu at the university finished in 1966.At the invitation of Professor Jacques-Louis Lions, Professor Livisited the prestigious Collège de France, Paris, France, as avisiting scholar from January 1979 to April 1981. He was promoted tobe a Full Professor of Mathematics in 1980, became a Ph.D.Supervisor for Pure Mathematics in 1981 and Applied Mathematics in1983 respectively, and was appointed as the Dean of Graduate Schoolof Fudan University from 1991 to 1999. Professor Li was elected as aMember of the Chinese Academy of Sciences in 1995, a Fellow of theThird World Academy of Sciences (the Academy of Sciences for theDeveloping World) in 1997, a Foreign Member of the French Academy ofSciences in 2005 and a Member of the European Academy of Sciences in2007.For more information please click the “Full Text” above.

On the formula of Jacques-Louis Lions for reproducing kernels of harmonic and other functions

Article On the formula of Jacques-Louis Lions for reproducing kernels of harmonic and other functions was published on June 1, 2004 in the journal Journal für die reine und angewandte Mathematik (volume 2004, issue 570).

Dedication to Jacques-Louis Lions

Dedication to Jacques-Louis Lions

Jacques-Louis LIONS, 1928-2001

Jacques-Louis Lions was born in the heart of Provence in the charming city of Grasse,much renowned for its perfume industry and its historical center.In spite of his young age, he had the courage and determination to join the FrenchResistance at the end of 1943, as a soldier in the FFI (French Forces of the Interior). Therehe met Andree, his wife and life-long companion.

Jacques-Louis Lions. 2 May 1928 – 17 May 2001

Jacques-Louis Lions was born in the heart of Provence in the charming city of Grasse, much renowned for its perfume industry and its historical centre. In spite of his young age, he had the courage and determination to join the French Résistance at the end of 1943, as a soldier in the FFI (French Forces of the Interior). There he met Andrée, his wife and lifelong companion. Their son Pierre-Louis, who was born in 1956, would also be distinguished by mathematical talent. This gift earned him the highest mathematical distinction, the Fields Medal, awarded to him during the 1994 International Congress of Mathematicians in Zurich. His parents had the great joy of being present for this unique occasion.

Mathematical Analysis and Numerical Methods for Science and Technology Vol. 4. Integral Equations and Numerical Methods for Science and Technology (Robert Dautray and Jacques-Louis Lions) (John C. Amson translator)

Mathematical Analysis and Numerical Methods for Science and Technology Vol. 4. Integral Equations and Numerical Methods for Science and Technology (Robert Dautray and Jacques-Louis Lions) (John C. Amson translator)

Mathematical Analysis and Numerical Methods for Science and Technology, Volume 2: Functional and Variational Methods (Robert Daut ray and Jacques-Louis Lions; Ian N. Sneddon, trans.)

Mathematical Analysis and Numerical Methods for Science and Technology, Volume 2: Functional and Variational Methods (Robert Daut ray and Jacques-Louis Lions; Ian N. Sneddon, trans.)