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.
By:
Luigi Ambrosio,
Norman Dancer
Edited by:
Giuseppe Buttazzo,
Antonio Marino,
M.K.V. Murthy
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: Softcover reprint of the original 1st ed. 2000
Dimensions:
Height: 235mm,
Width: 155mm,
Spine: 19mm
Weight: 1.130kg
ISBN: 9783540648031
ISBN 10: 3540648038
Pages: 348
Publication Date: 24 January 2000
Audience:
College/higher education
,
Professional and scholarly
,
Professional & Vocational
,
A / AS level
,
Further / Higher Education
Format: Paperback
Publisher's Status: Active
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.
Reviews for Calculus of Variations and Partial Differential Equations: Topics on Geometrical Evolution Problems and Degree Theory
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. Fur Interessierte eine lohnenswerte Anschaffung! Jahresbericht der DMV, 104. Band, Heft 2, August 2002
