Author : Joe Geisbauer
Publisher :
ISBN 13 : 9781303021107
Total Pages : 124 pages
Book Rating : 4.0/5 (211 download)
Book Synopsis Regularity for Solutions to Parabolic Systems and Nonlocal Minimization Problems by : Joe Geisbauer
Download or read book Regularity for Solutions to Parabolic Systems and Nonlocal Minimization Problems written by Joe Geisbauer and published by . This book was released on 2013 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this dissertation is to contribute to both the nonlocal and the local settings of regularity theory within the calculus of variations. In the nonlocal theory, we first establish the existence of minimizers for two classes of functionals. However, the main result of Chapter 2 states an analogue for higher differentiability of minimizers in the setting of nonlocal functionals, which is established through an application of the difference quotient method. This nonlocal analogue is stated in terms of the fractional order difference quotient, which corresponds to the order of the Besov space to which the solution belongs.