Calculus of variations and partial differential equations : topics on geometrical evolution problems and degree theory
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書誌事項
Calculus of variations and partial differential equations : topics on geometrical evolution problems and degree theory
Springer, c2000
- : softcover
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注記
Includes bibliographical references and index
List of authors -- p. [ix]
"The project of editing this book originated in a two-week Summer School on "Calculus of Variations and Partial Differential Equations" which was held in Pisa in September 1996" -- Pref
内容説明・目次
内容説明
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.
目次
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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