By Giovanni Leoni
Sobolev areas are a primary software within the sleek examine of partial differential equations. during this booklet, Leoni takes a singular method of the speculation by means of taking a look at Sobolev areas because the normal improvement of monotone, totally non-stop, and BV features of 1 variable. during this means, the vast majority of the textual content will be learn with out the prerequisite of a path in sensible research. the 1st a part of this article is dedicated to learning capabilities of 1 variable. numerous of the themes handled ensue in classes on genuine research or degree thought. right here, the point of view emphasizes their functions to Sobolev services, giving a truly various style to the remedy. This straightforward begin to the booklet makes it appropriate for complex undergraduates or starting graduate scholars. furthermore, the one-variable a part of the ebook is helping to improve a great historical past that allows the analyzing and realizing of Sobolev capabilities of numerous variables. the second one a part of the booklet is extra classical, even though it additionally comprises a few fresh effects. along with the normal effects on Sobolev services, this a part of the publication comprises chapters on BV capabilities, symmetric rearrangement, and Besov areas. The publication includes over two hundred routines.