Partial Differential Equations of Elliptic Type (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 2)

In the theory of partial differential equations, the study of elliptic equations occupies a preeminent position, both because of the importance which it assumes for various questions in mathematical physics, and because of the completeness of the results obtained up to the present time. In spite of this, even in the more classical treatises on analysis the theory of elliptic equations has been considered and illustrated only from particular points of view, while the only expositions of the whole theory, the extremely valuable ones by LICHTENSTEIN and AscoLI, have the charac­ ter of encyclopedia articles and date back to many years ago. Consequently it seemed to me that it would be of some interest to try to give an up-to-date picture of the present state of research in this area in a monograph which, without attaining the dimensions of a treatise, would nevertheless be sufficiently extensive to allow the expo­ sition, in some cases in summary form, of the various techniques used in the study of these equations. Front Matter....Pages I-XII Boundary value problems for linear equations....Pages 1-22 Functions represented by integrals....Pages 23-48 Transformation of the boundary value problems into integral equations....Pages 49-96 Generalized solutions of the boundary value problems....Pages 97-145 A priori majorization of the solutions of the boundary value problems....Pages 146-179 Nonlinear equations....Pages 180-222 Other research on equations of second order. Equations of higher order. Systems of equations.....Pages 223-288 Back Matter....Pages 289-372