By Ennio De Giorgi; et al
The e-book incorporates a collection of forty three medical papers of the good mathematician Ennio De Giorgi. All papers are written in English and 17 of them seem additionally of their unique Italian model. The editors supply additionally a brief biography of Ennio De Giorgi and a close account of his medical achievements, starting from his seminal paper at the resolution of Hilbert's nineteenth challenge to the idea of perimeter and minimum surfaces, the speculation of G-convergence and the principles of arithmetic.
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Extra info for Selected papers
N. This description is much simpler than the one obtained through the parametric representation of the surfaces, particularly in codimensions larger than one. 3 Minimizing movements In 1992 De Giorgi proposed a general method for the study of steepest descent curves of a functional F in a metric space (X, d). 6. The work on Foundations of Mathematics 33 a recursive minimization scheme (corresponding in the classical cases to Euler’s implicit method), inspired by a time discretization of the mean curvature motion introduced by Frederick J.
The paper  introduces the notion of (p, q)-convex function on a Hilbert space and proves an existence and uniqueness theorem for the corresponding evolution equations. These results are extended in  to nonconvex functions of more general type, and to a wide class of nonmonotone operators. Besides the classical case, where one considers the sum of a convex function and of a smooth function, these results can be applied to many other problems with a nonconvex and nondiﬀerentiable constraint.
When the random functionals are not equi-coercive, the space of functionals can still be equipped with a topology related to Γ-convergence, but this topology is no longer metrizable, and, although it satisﬁes the Hausdorﬀ separation axiom, it exhibits some pathological properties, which imply that the only continuous functions on this space are constant. In the paper  De Giorgi proposes several notions of convergence for measures deﬁned on the space of lower semicontinuous functions, and formulates some problems whose solution would enable one to determine the most suitable notion of convergence for the study of Γ-limits of random functionals.
Selected papers by Ennio De Giorgi; et al