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Book review

Author(s) Alvino, A. (ed.)
Fabes, E. (ed.)
Talenti, G. (ed.)
Title Partial Differential Equations of Elliptic Type
Publisher Cambridge University Press
Year of publication 1994
Reviewed by Paul Blaga

This book collects the papers presented at a conference on elliptic-type partial differential equations (ETPDE), organized by the Istituto Nazionale di Alta Matematica in October, 1992 and held at Cortona, Italy.

The first aim of the conference was to offer to a number of respected experts in the field the opportunity to meet and exchange ideas.

The volume includes eleven papers related to ETPDE, especially to geometric aspects of these equations. There is no room to list here their titles or to even attempt a description of their contents. Anyway, I'll mention, at least, some of the topics touched. Thus, the reader can find discussions on topics as: isoperimetric inequalities, prescribed scalar curvature, symmetrisation, quasilinear elliptic problems with boundary blow-up, the inverse conductivity problem, the motion of an ideal incompressible fluid, the existence of convex hypersurfaces with prescribed mean curvature, eigenvalue problems, differential geometric methods in the design of reflector antennas. The papers include both new results (many of them belonging to authors) and new points of view on some older one. Each one ends with a list of references. They have an expository nature and are quite comprehensive. The special interest of most papers for the geometrical aspects confers to the volume a unitary character. The readers (from graduate students to researchers) could hardly found in other place such a clear account of the latest achievements in this very active field of mathematics.

Let me finish by emphasizing the excellent technical conditions of the book.