Background
Fonseca was born in Portugal, and did her undergraduate studies at the University of Lisbon.
(In recent years the need to extend the notion of degree t...)
In recent years the need to extend the notion of degree to nonsmooth functions has been triggered by developments in nonlinear analysis and some of its applications. This new study relates several approaches to degree theory for continuous functions and incorporates newly obtained results for Sobolev functions. These results are put to use in the study of variational principles in nonlinear elasticity. Several applications of the degree are illustrated in the theories of ordinary and partial differential equations. Other topics include multiplication theorem, Hopf's theorem, Brower's fixed point theorem, odd mappings, and Jordan's separation theorem, all suitable for graduate courses in degree theory and application.
http://www.amazon.com/gp/product/0198511965/?tag=2022091-20
( This is the first of two books on methods and technique...)
This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.
http://www.amazon.com/gp/product/038735784X/?tag=2022091-20
Fonseca was born in Portugal, and did her undergraduate studies at the University of Lisbon.
She earned a Doctor of Philosophy from the University of Minnesota in 1985, under the supervision of David Kinderlehrer, who later followed his student to Carnegie Mellon University.
She joined the Carnegie Mellon University faculty after postdoctoral studies in Paris, France. In 2011, Fonseca was elected president of the Society for Industrial and Applied Mathematics. Fonseca is a knight of the Order of Saint James of the Sword.
Fonseca is married to stem cell researcher Gerald Schatten.
(In recent years the need to extend the notion of degree t...)
( This is the first of two books on methods and technique...)
American Mathematical Society.