Elementary Description of Principal Results

Abstract

Chapter 1 is intended for those who want to acquire, as quickly as possible, a knowledge of the basic elements and results of the theory of elliptic equations; naturally, it is therefore reduced to the exposition of only the most important and easy results. We also have in mind non-mathematician readers whose interest is oriented more towards applications and numerical methods. Nevertheless, reading Chap. 1 is recommended to those who will study the following chapters to familiarize themselves with the basic notions which theory will meet again in the rest of the book. For the moment, we will limit ourselves to citing only the works of R. Courant and D. Hilbert [1]; S. G. Mikhlin [2]; E. Magenes and G. Stampacchia [1], where further literature can be found, and to S. Agmon [4]; J.L. Lions [4]; V. I. Smirnov [1]; S. L. Sobolev [1]; G. Hellwig [1].