An inverse problem for the minimal surface equation
Nurminen, J. (2023). An inverse problem for the minimal surface equation. Nonlinear Analysis : Theory, Methods and Applications, 227, Article 113163. https://doi.org/10.1016/j.na.2022.113163
© 2022 The Author(s). Published by Elsevier Ltd.
We use the method of higher order linearization to study an inverse boundary value problem for the minimal surface equation on a Riemannian manifold , where the metric is conformally Euclidean. In particular we show that with the knowledge of Dirichlet-to-Neumann map associated to the minimal surface equation, one can determine the Taylor series of the conformal factor at up to a multiplicative constant. We show this both in the full data case and in some partial data cases.
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland
Funding program(s)Centre of Excellence, AoF
Additional information about fundingThe author was supported by the Finnish Centre of Excellence in Inverse Modelling and Imaging (Academy of Finland grant 284715).
Showing items with similar title or keywords.
Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations Lassas, Matti; Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko (European Mathematical Society Publishing House, 2021)We study various partial data inverse boundary value problems for the semilinear elliptic equation Δu + a(x, u) = 0 in a domain in Rn by using the higher order linearization technique introduced by Lassas– Liimatainen–Lin–Salo ...
Lassas, Matti; Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko (Elsevier, 2021)We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for ...
Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko; Tyni, Teemu (Elsevier, 2022)We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps us to solve inverse problems for certain ...
Guillarmou, Colin; Salo, Mikko; Tzou, Leo (Springer, 2019)In this note we show that on any compact subdomain of a K¨ahler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to ...
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities Lu, Shuai; Salo, Mikko; Xu, Boxi (IOP Publishing, 2022)We consider increasing stability in the inverse Schrödinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential ...