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Variational Analysis in Sobolev and BV Spaces
This self-contained book is excellent for graduate-level courses devoted to variational analysis, optimization, and partial differential equations (PDEs). It provides readers with a complete guide to problems in these fields as well as a detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. It contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references. The book is divided into two parts. In Part I, classical Sobolev spaces are introduced and the reader is provided with the basic tools and methods of variational analysis and optimization in infinite dimensional spaces, with applications to classical PDE problems. In Part II, BV spaces are introduced and new trends in variational analysis are presented.
One-dimensional Variational Problems
While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.
Nonlinear Analysis and Continuum Mechanics
The chapters in this volume deal with four fields with deep historical roots that remain active areas reasearch: partial differential equations, variational methods, fluid mechanics, and thermodynamics. The collection is intended to serve two purposes: First, to honor James Serrin, in whose work the four fields frequently interacted; and second, to bring together work in fields that are usually pursued independently but that remain remarkably interrelated. Serrin's contributions to mathematical analysis and its applications are fundamental and include such theorems and methods as the Gilbarg- Serrin theorem on isoated singularities, the Serrin symmetry theorem, the Alexandrov-Serrin moving-plane technique, The Peletier-Serrin uniqueness theorem, and the Serrin integal of the calculus of variations. Serrin has also been noted for the elegance of his mathematical work and for the effectiveness of his teaching and collaborations.
Variational Methods in Shape Optimization Problems
Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
Variational Analysis in Sobolev and BV Spaces
This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision.
Developments in Partial Differential Equations and Applications to Mathematical Physics
During the days 14-18 of October 1991, we had the pleasure of attending a most interesting Conference on New Developments in Partial Differential Equations and Applications to Mathematical Physics in Ferrarra. The Conference was organized within the Scientific Program celebrating the six hundredth birthday of the University of Ferrarra and, after the many stimulating lectures and fruitful discussions, we may certainly conclude, together with the numerous participants, that it has represented a big success. The Conference would not have been possible without the financial support of several sources. In this respect, we are particularly grateful to the Comitato Organizzatore del VI Centenario,...
Variational Analysis and Aerospace Engineering
"This volume collects the contributions presented in the workshop on "Variational Analysis and Aerospace Engineering," held in Erice, Italy on September 8-16, 2007 at the International School of Mathematics, Guido Stampacchia. The worshop provided a platform for aerospace engineers and mathematicians to discuss the advance problems requiring an extensive application of mathematics."--P. [4] of cover.
Calculus of Variations and Partial Differential Equations
At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.
Variational Analysis and Aerospace Engineering: Mathematical Challenges for Aerospace Design
This volume consists of papers presented at the Variational Analysis and Aerospace Engineering Workshop II held in Erice, Italy in September 2010 at the International School of Mathematics "Guido Stampacchia". The workshop provided a platform for aerospace engineers and mathematicians (from universities, research centers and industry) to discuss the advanced problems requiring an extensive application of mathematics. The presentations were dedicated to the most advanced subjects in engineering and, in particular to computational fluid dynamics methods, introduction of new materials, optimization in aerodynamics, structural optimization, space missions, flight mechanics, control theory and optimization, variational methods and applications, etc. This book will capture the interest of researchers from both academia and industry.
Optimal Transportation and Applications
Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.
