6533b7dafe1ef96bd126d879

RESEARCH PRODUCT

Enclosure method for the p-Laplace equation

Manas KarMikko SaloTommi Brander

subject

Convex hullGeneralization35R30 (Primary) 35J92 (Secondary)EnclosureMathematics::Classical Analysis and ODEsInverseMonotonic function01 natural sciencesTheoretical Computer ScienceMathematics - Analysis of PDEsFOS: Mathematics0101 mathematicsMathematical PhysicsMathematicsLaplace's equationMathematics::Functional AnalysisCalderón problemApplied Mathematics010102 general mathematicsMathematical analysisComputer Science Applications010101 applied mathematicsNonlinear systemSignal ProcessingJumpp-Laplace equationenclosure methodAnalysis of PDEs (math.AP)

description

We study the enclosure method for the p-Calder\'on problem, which is a nonlinear generalization of the inverse conductivity problem due to Calder\'on 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.

yearjournalcountryeditionlanguage
2014-10-15
https://dx.doi.org/10.48550/arxiv.1410.4048