Closures of planar BV homeomorphisms and the relaxation of functionals with linear growth

Abstract: Motivated by relaxation results of Kristensen and Rindler, and of Benešová, Krömer and Kružík for BV maps, we study the class of strict limits of BV planar homeomorphisms. We show that, although such maps need not be injective and are not necessarily continuous on almost every line, the class has a reasonable behavior expected for limit of elastic deformations. By a characterization of the classes of strict and area-strict limits of BV homeomorphisms we show that these classes coincide.

This is based on joint works with S. Hencl, A. Kauranen and E. Radici.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).