Details

Autor(en) / Beteiligte

• Ambrosio, Luigi
• Dancer, Norman
• Buttazzo, Giuseppe[Herausgeber]
• Marino, Antonio[Herausgeber]
• Murthy, M.K.V[Herausgeber]

Titel

Calculus of Variations and Partial Differential Equations : Topics on Geometrical Evolution Problems and Degree Theory [electronic resource]

Auflage

1st ed. 2000

Ort / Verlag

Berlin, Heidelberg : Springer Berlin Heidelberg

Erscheinungsjahr

2000

Beschreibungen/Notizen

• Bibliographic Level Mode of Issuance: Monograph
• Includes bibliographical references and index.
• 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.
• 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.
• English