This note contains an expanded version of the lecture delivered at the "Renato Caccioppoli Conference" (Naples, September 23-25, 2004). I review the definition and main properties of the distributional Jacobians, in particular for Sobolev maps u from R^n to R^k with values in the (k-1)-dimensional sphere. We show that the Jacobian si supported on the singular set of u and represents the part of the singularity which is topologically necessary. Some of the results from a joint paper with S. Baldo and G. Orlandi (Functions with prescribed singularties) concerning the construction of maps valued in spheres with prescribed singularity are described in the last section.
Distributional Jacobian and singularities of Sobolev maps
ALBERTI, GIOVANNI
2005-01-01
Abstract
This note contains an expanded version of the lecture delivered at the "Renato Caccioppoli Conference" (Naples, September 23-25, 2004). I review the definition and main properties of the distributional Jacobians, in particular for Sobolev maps u from R^n to R^k with values in the (k-1)-dimensional sphere. We show that the Jacobian si supported on the singular set of u and represents the part of the singularity which is topologically necessary. Some of the results from a joint paper with S. Baldo and G. Orlandi (Functions with prescribed singularties) concerning the construction of maps valued in spheres with prescribed singularity are described in the last section.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
