6533b85ffe1ef96bd12c1aff
RESEARCH PRODUCT
Superconductive and insulating inclusions for linear and non-linear conductivity equations
Tommi BranderManas KarJoonas Ilmavirtasubject
Pure mathematicsControl and Optimizationmedia_common.quotation_subjectMathematics::Analysis of PDEsBoundary (topology)probe methodConductivity01 natural sciencesMathematics - Analysis of PDEs35R30 35J92 (Primary) 35H99 (Secondary)FOS: MathematicsDiscrete Mathematics and CombinatoricsPharmacology (medical)Nabla symbol0101 mathematicsmedia_commonp-harmonic functionsLaplace's equationPhysicsPartial differential equationCalderón problemComputer Science::Information Retrieval010102 general mathematicsta111Zero (complex analysis)Infinity3. Good health010101 applied mathematicsNonlinear systeminclusionModeling and Simulationinverse boundary value problemAnalysisinkluusioAnalysis of PDEs (math.AP)enclosure methoddescription
We detect an inclusion with infinite conductivity from boundary measurements represented by the Dirichlet-to-Neumann map for the conductivity equation. We use both the enclosure method and the probe method. We use the enclosure method to prove partial results when the underlying equation is the quasilinear $p$-Laplace equation. Further, we rigorously treat the forward problem for the partial differential equation $\operatorname{div}(\sigma\lvert\nabla u\rvert^{p-2}\nabla u)=0$ where the measurable conductivity $\sigma\colon\Omega\to[0,\infty]$ is zero or infinity in large sets and $1<p<\infty$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-10-30 |