By L. E. Fraenkel
This ebook provides the fundamental thought of the symmetry of ideas to second-order elliptic partial differential equations by way of the utmost precept. It proceeds from straight forward evidence in regards to the linear case to contemporary effects approximately optimistic ideas of nonlinear elliptic equations. Gidas, Ni and Nirenberg, construction at the paintings of Alexandrov and Serrin, have proven that the form of the set on which such elliptic equations are solved has a powerful influence at the type of optimistic strategies. specifically, if the equation and its boundary let spherically symmetric options, then, remarkably, all optimistic strategies are spherically symmetric. those fresh and significant effects are awarded with minimum necessities, in a mode suited for graduate scholars. lengthy appendices supply a leisurely account of uncomplicated proof concerning the Laplace and Poisson equations, and there's an abundance of workouts, with specific tricks, a few of which comprise new effects.