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

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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.

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Editorial Reviews

From the Publisher
"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
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Product Details

  • ISBN-13: 9783540648031
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 3/1/2000
  • Series: Universitext Series
  • Edition description: Softcover reprint of the original 1st ed. 2000
  • Edition number: 1
  • Pages: 348
  • Product dimensions: 0.75 (w) x 9.21 (h) x 6.14 (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.

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