Abstract
In this paper we consider the PDE system of vanishing normal projection of the Laplacian for maps :
This system has discontinuous coefficients and geometrically expresses the fact that the Laplacian is a vector field tangential to the image of the mapping. It arises as a constituent component of the -Laplace system for all . For , the -Laplace system is the archetypal equation describing extrema of supremal functionals in vectorial calculus of variations in . Herein we show that the image of a solution is piecewise affine if either the rank of is equal to one or and has additively separated form. As a consequence we obtain corresponding flatness results for -Harmonic maps for .
Citation
Hussien Abugirda. Birzhan Ayanbayev. Nikos Katzourakis. "Rigidity and flatness of the image of certain classes of mappings having tangential Laplacian." Rocky Mountain J. Math. 50 (2) 383 - 396, April 2020. https://doi.org/10.1216/rmj.2020.50.383
Information