Enclosure method for the p-Laplace equation. (20th February 2015)

• Record Type: Journal Article
• Authors: Brander, Tommi; Kar, Manas; Salo, Mikko
• Is Part Of: Inverse problems. Volume 31:Number 4(2015:Apr.)
• Publication Date: 2015-02-20
• Subjects: enclosure method -- p-Laplace equation -- Calderón's problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/4/045001
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We study the enclosure method for the p -Calderón problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderón 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.