6533b871fe1ef96bd12d252a

RESEARCH PRODUCT

Monotonicity and enclosure methods for the p-Laplace equation

Manas KarTommi BranderMikko SaloBastian Harrach

subject

Convex hull35R30 (Primary) 35J92 (Secondary)EnclosurePerturbation (astronomy)Monotonic function01 natural sciencesConstructiveMathematics - Analysis of PDEsEnclosure methodFOS: Mathematics0101 mathematicsMathematicsInclusion detectionMonotonicity methodLaplace's equationmonotonicity methodApplied Mathematics010102 general mathematicsMathematical analysista111inclusion detection010101 applied mathematicsNonlinear systemMonotone polygonp-Laplace equationAnalysis of PDEs (math.AP)enclosure method

description

We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of which is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.

yearjournalcountryeditionlanguage
2018-01-01
10.1137/17m1128599https://orbit.dtu.dk/en/publications/c0c9508f-7a38-43a2-b9e3-7f1c3ea0beb4