Luigi Ambrosio, Norman Dancer

Calculus of Variations and Partial Differential Equations

Topics on Geometrical Evolution Problems and Degree Theory
Herausgeber: Murthy, M. K. V.; Buttazzo, Giuseppe; Marino, Antonio

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-64803-1
• 2000.
• Seitenzahl: 360
• Erscheinungstermin: 24. Januar 2000
• Englisch
• Abmessung: 235mm x 155mm x 20mm
• Gewicht: 550g
• ISBN-13: 9783540648031
• ISBN-10: 3540648038
• Artikelnr.: 08032782

Inhaltsangabe

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.

Rezensionen

"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