Lieberstein H.M. Theory of partial differential equations

Academic Press, 1972. — 299 p.
This book is written in four modular parts intended as easy steps for the student. The intention here is to lead him from an elementary level to a level of modern analysis research. Thus the first pages of Part I are an explanation of the regular (classical) solutions of the second-order wave equation in two-space-time, while the latter pages of Part IV encompass a more or less complete analysis of the existence of LP-weak solutions for boundary-value problems for equations of elliptic-parabolic type expounded according to G. Fichera of the University of Rome. In the developing process, an effort is made to ensure that the student samples the extensive variety of mathematically conceivable boundary-value problems, even if their properties are not entirely satisfying once analyzed, and that he learns how to use these tools to elucidate phenomena of nature and technology.