偏微分方程

《偏微分方程(第2卷)(英文)》主要內容簡介：In this second volume, FUNCTIONAL ANALYTIC METHODS, we continue our textbook PARTIAL DIFFERENTIAL EQUATIONS OF GEOMETRY AND PHYSICS.From both areas we shall answer central questions such as curvature estimates or eigenvalue problems, for instance. With the title of our textbook we also want to emphasize the pure and applied aspects of partial differential equa-tions. It turns out that the concepts of solutions are permanently extended ia the theory of partial differential equations. Here the classical methods do not lose their significance. Besides the n-dimensional theory we equally want to present the two-dimensional theory - so important to our geometric intuition.We shall solve the differential equations by the continuity method, the vari-ational method or the topological method. The continuity method may be preferred from a geometric point of view, since the stability of the solution is investigated there. The variational method is very attractive from the physi-cal point of view; however, difficult regularity questions for the weak solution appear with this method. The topological method controls the whole set of solutions during the deformation of the problem, and does not depend onuniqueness as does the variational method.