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• 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 ...

• Estimates of the modeling error generated by homogenization of an elliptic boundary value problem 

  Repin, Sergey; Samrowski, Tatiana; Sauter, Stefan (Walter de Gruyter GmbH & Co. KG, 2016)

  In this paper, we derive a posteriori bounds of the di erence between the exact solution of an elliptic boundary value problem with periodic coe cients and an abridged model, which follows from the homogenization theory. ...

• Inverse problems for elliptic equations with power type nonlinearities 

  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 ...

• Inverse problems for elliptic equations with fractional power type nonlinearities 

  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 ...

• Inverse problems for semilinear elliptic PDE with measurements at a single point 

  Salo, Mikko; Tzou, Leo (American Mathematical Society (AMS), 2023)

  We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined ...