A compactness result is proved for SBV, the space of special functions of bounded variation. It is shown that a sequence of functions of SBV on an open, bounded domain with Lipschitz boundary with three quantities bounded will have a subsequence that weakly converges in BV to a function that is also in SBV. This theorem has implications for the existence of desired solutions in problems from the calculus of variations.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Howard, Thomas T.

Publisher

• Worcester Polytechnic Institute

Identifier

• 05D370M

Advisor

• Larsen, Christopher J.

Year

• 2005

Date created

• 2005-01-01

Resource type

• Major Qualifying Project

Major

• Physics

Rights statement

• In Copyright