Inverse problems for p-Laplace type equations under monotonicity assumptions

2016/02/08 by Chang-Yu Guo, Chang‐Yu Guo, Guo, Chang-Yu +4
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP

paper · pdf · doi:10.48550/arxiv.1602.02591

17 pages

openalex publication_date 2016/02/08 · arxiv created 2016/03/14 · arxiv updated 2016/03/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider inverse problems for p-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying σ₁ ≥ σ₂ and having the same nonlinear Dirichlet-to-Neumann map must be identical. The proof is based on a monotonicity inequality and the unique continuation principle for p-Laplace type equations. In higher dimensions, where unique continuation is not known, we obtain a similar result for conductivities close to constant.

Citations

• Boundary regularity for solutions of degenerate elliptic equations

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