An Introduction to Sobolev Spaces and Interpolation Spaces

This volume appears parallel to the conference in honor of Luc Tartar on the occasion of his 60th birthday held in Paris, July 2007 at the CMAP of the Ecole Polytechnique.

Partly in collaboration with François Murat, Luc Tartar has specialized in the development of new mathematical tools for solving the partial differential equations of continuum mechanics (homogenization, compensated compactness, H-measures), pioneering the study of microstructures compatible with the partial differential equations describing the physical balance laws, and the constitutive relations.

He likes to point out the defects of many of the models which are used, as a natural way to achieve the goal of improving our understanding of mathematics and of continuum mechanics.

Appears parallel to the conference in honour of Luc Tartar on the ocasion of his 60th birthday held in Paris, July 2-6, 2007 at the CMAP of the Ecole Polytechnique During his long career, Luc Tartar had not written a book until 2006 when the new series Lecture Notes of the Unione Matematica Italiana started publication. This is his second volume in the new series and a third is in preparation Includes supplementary material: sn.pub/extras

Auteur

Luc Tartar studied at Ecole Polytechnique in Paris, France, 1965-1967, where he was taught by Laurent Schwartz and Jacques-Louis Lions in mathematics, and by Jean Mandel in continuum mechanics.

He did research at Centre National de la Recherche Scientifique, Paris, France, 1968-1971, working under the direction of Jacques-Louis Lions for his thèse d'état, 1971.

He taught at Université Paris IX-Dauphine, Paris, France, 1971-1974, at University of Wisconsin, Madison, WI, 1974-1975, at Université de Paris-Sud, Orsay, France, 1975-1982.

He did research at Commissariat à l'Energie Atomique, Limeil, France, 1982-1987.

In 1987, he was elected Correspondant de l'Académie des Sciences, Paris, in the section Mécanique.

Since 1987 he has been teaching at Carnegie Mellon University, Pittsburgh, PA, where he has been University Professor of Mathematics since 1994.

Partly in collaboration with François Murat, he has specialized in the development of new mathematical tools for solving the partial differential equations of continuum mechanics (homogenization, compensated compactness, H-measures), pioneering the study of microstructures compatible with the partial differential equations describing the physical balance laws, and the constitutive relations.

He likes to point out the defects of many of the models which are used, as a natural way to achieve the goal of improving our understanding of mathematics and of continuum mechanics.

Contenu
Historical Background.- The Lebesgue Measure, Convolution.- Smoothing by Convolution.- Truncation; Radon Measures; Distributions.- Sobolev Spaces; Multiplication by Smooth Functions.- Density of Tensor Products; Consequences.- Extending the Notion of Support.- Sobolev's Embedding Theorem, 1 ?