Author	Ambrosio, Luigi. author
Title	Calculus of Variations and Partial Differential Equations [electronic resource] : Topics on Geometrical Evolution Problems and Degree Theory / by Luigi Ambrosio, Norman Dancer ; edited by Giuseppe Buttazzo, Antonio Marino, M. K. V. Murthy
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000
Connect to	http://dx.doi.org/10.1007/978-3-642-57186-2
Descript	X, 348 p. 4 illus. online resource

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

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 Giorgiโs 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

1. Mathematics
2. System theory
3. Calculus of variations
4. Mathematics
5. Calculus of Variations and Optimal Control; Optimization
6. Systems Theory
7. Control