Some Asymptotic Problems in the Theory of Partial Differential Equations [Paperback]

In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more.The author's work in the area of partial differential equations is highlighted in a collection divided into two distinctive parts. Because many of the results have not appeared in book form before, new light is accordingly shed on the subject and new ideas and problems raised.The author's work in the area of partial differential equations is highlighted in a collection divided into two distinctive parts. Because many of the results have not appeared in book form before, new light is accordingly shed on the subject and new ideas and problems raised.In this book, Professor Oleinik highlights her work in the area of partial differential equations. The book is divided into two parts: the first is devoted to the study of the asymptotic behavior at infinity of solutions of a class of nonlinear second order elliptic equations in unbounded and, in particular, cylindrical domains. The second contains the most recent results of the author in the theory of homogenization of partial differential equations and is concerned with questions about partially perforated domains and of solutions with rapidly alternating types of boundary conditions. Many of the results here have not appeared in book form before, and it sheds new light on the subject, raising many new ideas and open problems.Preface; 1. Asymptotic problems for non-linear elliptic equations; 2. On the asymptotic behaviour of solutions of some non-linear elliptic equations in cylindrical domains; 3. On the asymptotic behaviour of solutions of non-linear elliptic equations in a neighbourhood of a conic point of the boundary; 4. On some homogenization problems; Index.'Warmly recommended.' H. P. Urbach, ITW Nieuws'& can be recommended to graduate students or anyone who wants to become familiar with PDE techniques.' Catherine Bandle, Bulletin of the Londolˆ