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＜E-Book＞
Calculus of Variations and Partial Differential Equations : Topics on Geometrical Evolution Problems and Degree Theory / by Luigi Ambrosio, Norman Dancer ; edited by Giuseppe Buttazzo, Antonio Marino, M.K.V. Murthy

Edition	1st ed. 2000.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2000
Language	English
Size	X, 348 p. 4 illus : online resource
Authors	*Ambrosio, Luigi author Dancer, Norman author Buttazzo, Giuseppe editor Marino, Antonio editor Murthy, M.K.V editor SpringerLink (Online service)
Subjects	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:System theory LCSH:Control theory FREE:Calculus of Variations and Optimization FREE:Systems Theory, Control
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-642-57186-2

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