Enclosure method for the p-Laplace equation
Brander, T., Kar, M., & Salo, M. (2015). Enclosure method for the p-Laplace equation. Inverse Problems, 31 (4), 045001. doi:10.1088/0266-5611/31/4/045001 Retrieved from http://arxiv.org/abs/1410.4048
Published in
Inverse ProblemsDate
2015Discipline
MatematiikkaCopyright
© Institute of Physics Publishing Ltd. and Institute of Physics 2015. This is a final draft version of an article whose final and definitive form has been published by Institute of Physics Publishing Ltd. and Institute of Physics.
Abstract. We study the enclosure method for the p-Calderon
problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderon that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, where the inclusion is modelled as a jump in the conductivity. The result is based on a monotonicity inequality
and the properties of the Wolff solutions.