Calculus of Variations and Geometric Measure Theory

M. Giaquinta - D. Mucci

Maps into manifolds and currents: area and $W^{1,2}$-, $W^{1/2}$-, $BV$-energies

created by mucci on 09 Oct 2006


Edizioni della Normale. CRM Series. Scuola Normale Superiore Pisa

Inserted: 9 oct 2006

Year: 2006


This volume deals with the problem of characterizing the limit points of sequences of smooth maps from the unit ball of \,${R}^n$\, with values into a smooth boundaryless Riemannian manifold and with equibounded ''integral energies''. \par After surveying some known results about Cartesian currents and graphs with finite area and finite boundary area, we do characterize, as stated in the title, weak limits of sequences of smooth maps with equibounded \,$W^{1,2}$-, \,$W^{1/2}$-, or \,$BV$-energies.