Calculus of Variations and Partial Differential Equations: Topics on Geometrical Evolution Problems and Degree Theory / Edition 1

by Luigi Ambrosio, Giuseppe Buttazzo, Norman Dancer, Antonio Marino, M.K.V. Murthy

Overview

The link between Calculus of Variations and Partial Differential Equations has always been strong, because variational problems produce, via their Euler-Lagrange equation, a differential equation and, conversely, a differential equation can often be studied by variational methods. At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on a classical topic (the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to pde's resp.), in a self-contained presentation accessible to PhD students, bridging the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and nicely 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.

Product Details

ISBN-13:	9783540648031
Publisher:	Springer Berlin Heidelberg
Publication date:	03/07/2000
Series:	Universitext Series
Edition description:	Softcover reprint of the original 1st ed. 2000
Pages:	348
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

I Geometric Evolution Problems.- Geometric evolution problems, distance function and viscosity solutions.- Variational models for phase transitions, an approach via—-convergence.- Some aspects of De Giorgi’s barriers for geometric evolutions.- Partial Regularity for Minimizers of Free Discontinuity Problems with p-th Growth.- Free discontinuity problems and their non-local approximation.- II Degree Theory on Convex Sets and Applications to Bifurcation.- Degree theory on convex sets and applications to bifurcation.- Nonlinear elliptic equations involving critical Sobolev exponents.- On the existence and multiplicity of positive solutions for semilinear mixed and Neumann elliptic problems.- Solitons and Relativistic Dynamics.- An algebraic approach to nonstandard analysis.- References.

Editorial Reviews

"Fazit: Dies ist kein typischer Proccedingsband, sondern stellt - insbesondere wegen der Lecture Notes von Dancer und vor allem wegen der von Ambrosio - ... eine wichtige Bereicherung der anspruchsvollen Forschungsliteratur auf den Gebieten Variationsrechnung und partielle Differentialgleichungen dar. Es ist erfreulich, dass hier allerneueste Forschungsergebnisse so schnell Eingang - abgesehen von Zeitschriften - in die Literatur gefunden haben. Für Interessierte eine lohnenswerte Anschaffung!"

Jahresbericht der DMV, 104. Band, Heft 2, August 2002

From the Publisher