Lauri Oksanen

I am a professor of applied mathematics and a member of the Centre of Excellence of Inverse Modelling and Imaging. For my preprints and publications as of September 2021 see below, for more recent preprints see arXiv.

My research interests include inverse problems for partial differential equations, their numerical analysis, and related geometric problems such as inversion of the geodesic ray transform. See my lecture notes of a summer school in 2018 at the Max Planck Institute in Leipzig for an introduction to these problems.

For contact information, see my profile.

Preprints

• E. Burman, A. Feizmohammadi, A. Munch, and L.O. Spacetime finite element methods for control problems subject to the wave equation. arXiv
• S. Alexakis, A. Feizmohammadi, and L.O. Lorentzian Calderon problem under curvature bounds. arXiv
• E. Burman, J. J. J. Gillissen, and L.O. Stability estimate for scalar image velocimetry. arXiv
• E. Burman, M. Nechita, and L.O. A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime. arXiv
• L.O., M. Salo, P. Stefanov, and G. Uhlmann. Inverse problems for real principal type operators. arXiv
• Y. Kurylev, M. Lassas, L.O., and G. Uhlmann. Inverse problem for Einstein-scalar field equations. arXiv

Publications

• X. Chen, M. Lassas, L.O., and G. P. Paternain. Detection of Hermitian connections in wave equations with cubic non-linearity. J. Eur. Math. Soc. (JEMS) (to appear), 2021-. arXiv
• A. Feizmohammadi, J. Ilmavirta, Y. Kian, and L.O. Recovery of time dependent coefficients from boundary data for hyperbolic equations. J. Spectr. Theory (to appear), 2021-. doi arXiv
• A. Feizmohammadi, M. Lassas, and L.O. Inverse problems for non-linear hyperbolic equations with disjoint sources and receivers. Forum Math. Pi (to appear), 2021-. arXiv
• A. Feizmohammadi and L.O. Recovery of zeroth order coefficients in non-linear wave equations. J. Inst. Math. Jussieu (to appear), 2021-. doi arXiv
• A. Kirpichnikova, J. Korpela, M. Lassas, and L.O. Construction of artificial point sources for a linear wave equation in unknown medium. SIAM J. Control Optim. (to appear), 2021-. arXiv
• T. Liimatainen and L.O. Counterexamples to inverse problems for the wave equation. Inverse Probl. Imaging (to appear), 2021-. arXiv
• E. Burman, A. Feizmohammadi, A. Munch, and L.O. Space time stabilized finite element methods for a unique continuation problem subject to the wave equation. ESAIM Math. Model. Numer. Anal., 55:S969–S991, 2021. doi arXiv
• X. Chen, M. Lassas, L.O., and G. P. Paternain. Inverse problem for the Yang-Mills equations. Comm. Math. Phys., 384(2):1187–1225, 2021. doi arXiv
• A. Feizmohammadi, J. Ilmavirta, and L.O. The light ray transform in stationary and static Lorentzian geometries. J. Geom. Anal., 31(4):3656–3682, 2021. doi arXiv
• A. Feizmohammadi, K. Krupchyk, L.O., and G. Uhlmann. Reconstruction in the Calderon problem on conformally transversally anisotropic manifolds. J. Funct. Anal., 281(9):109191, 25, 2021. doi arXiv
• E. Burman, A. Feizmohammadi, and L.O. A finite element data assimilation method for the wave equation. Math. Comp., 89(324):1681–1709, 2020. doi arXiv
• E. Burman, A. Feizmohammadi, and L.O. A fully discrete numerical control method for the wave equation. SIAM J. Control Optim., 58(3):1519–1546, 2020. doi arXiv
• E. Burman, M. Nechita, and L.O. A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime. Numer. Math., 144(3):451–477, 2020. doi arXiv
• C. I. Cârstea, G. Nakamura, and L.O. Uniqueness for the inverse boundary value problem of piecewise homogeneous anisotropic elasticity in the time domain. Trans. Amer. Math. Soc., 373(5):3423–3443, 2020. doi arXiv
• A. Feizmohammadi and L.O. An inverse problem for a semi-linear elliptic equation in Riemannian geometries. J. Differential Equations, 269(6):4683–4719, 2020. doi arXiv
• M. Lassas, L.O., P. Stefanov, and G. Uhlmann. The light ray transform on Lorentzian manifolds. Comm. Math. Phys., 377(2):1349–1379, 2020. doi arXiv
• E. Burman, M. Nechita, and L.O. Unique continuation for the Helmholtz equation using stabilized finite element methods. J. Math. Pures Appl. (9), 129:1–22, 2019. doi arXiv
• Y. Kian, Y. Kurylev, M. Lassas, and L.O. Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets. J. Differential Equations, 267(4):2210–2238, 2019. doi arXiv
• Y. Kian, M. Morancey, and L.O. Application of the boundary control method to partial data Borg-Levinson inverse spectral problem. Math. Control Relat. Fields, 9(2):289–312, 2019. doi arXiv
• Y. Kian and L.O. Recovery of time-dependent coefficient on Riemannian manifold for hyperbolic equations. Int. Math. Res. Not. IMRN, (16):5087–5126, 2019. doi arXiv
• J. Korpela, M. Lassas, and L.O. Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation. Inverse Probl. Imaging, 13(3):575–596, 2019. doi arXiv
• E. Burman, J. Ish-Horowicz, and L.O. Fully discrete finite element data assimilation method for the heat equation. ESAIM Math. Model. Numer. Anal., 52(5):2065–2082, 2018. doi arXiv
• E. Burman, M. G. Larson, and L.O. Primal-dual mixed finite element methods for the elliptic Cauchy problem. SIAM J. Numer. Anal., 56(6):3480–3509, 2018. doi arXiv
• E. Burman and L.O. Data assimilation for the heat equation using stabilized finite element methods. Numer. Math., 139(3):505–528, 2018. doi arXiv
• M. V. de Hoop, P. Kepley, and L.O. An exact redatuming procedure for the inverse boundary value problem for the wave equation. SIAM J. Appl. Math., 78(1):171–192, 2018. doi arXiv
• M. V. de Hoop, P. Kepley, and L.O. Recovery of a smooth metric via wave field and coordinate transformation reconstruction. SIAM J. Appl. Math., 78(4):1931–1953, 2018. doi arXiv
• T. Helin, M. Lassas, L.O., and T. Saksala. Correlation based passive imaging with a white noise source. J. Math. Pures Appl., 116:132–160, 2018. doi arXiv
• Y. Kian, L.O., E. Soccorsi, and M. Yamamoto. Global uniqueness in an inverse problem for time fractional diffusion equations. J. Differential Equations, 264(2):1146–1170, 2018. doi arXiv
• Y. Kurylev, L.O., and G. P. Paternain. Inverse problems for the connection Laplacian. J. Differential Geom., 110(3):457–494, 2018. doi arXiv
• M. Lassas, L.O., P. Stefanov, and G. Uhlmann. On the inverse problem of finding cosmic strings and other topological defects. Comm. Math. Phys., 357(2):569–595, 2018. doi arXiv
• O. Chervova and L.O. Time reversal method with stabilizing boundary conditions for photoacoustic tomography. Inverse Problems, 32(12):125004, 16, 2016. doi arXiv
• M. V. de Hoop, P. Kepley, and L.O. On the construction of virtual interior point source travel time distances from the hyperbolic Neumann-to-Dirichlet map. SIAM J. Appl. Math., 76(2):805–825, 2016. doi arXiv
• M. V. de Hoop, L.O., and J. Tittelfitz. Uniqueness for a seismic inverse source problem modeling a subsonic rupture. Comm. Partial Differential Equations, 41(12):1895–1917, 2016. doi arXiv
• J. Korpela, M. Lassas, and L.O. Regularization strategy for an inverse problem for a 1+1 dimensional wave equation. Inverse Problems, 32(6):065001, 24, 2016. doi arXiv
• M. Lassas, L.O., and Y. Yang. Determination of the spacetime from local time measurements. Math. Ann., 365(1-2):271–307, 2016. doi arXiv
• S. Liu and L.O. A Lipschitz stable reconstruction formula for the inverse problem for the wave equation. Trans. Amer. Math. Soc., 368(1):319–335, 2016. doi arXiv
• T. Helin, M. Lassas, and L.O. Inverse problem for the wave equation with a white noise source. Comm. Math. Phys., 332(3):933–953, 2014. doi arXiv
• M. Lassas and L.O. Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets. Duke Math. J., 163(6):1071–1103, 2014. doi arXiv
• L.O. and G. Uhlmann. Photoacoustic and thermoacoustic tomography with an uncertain wave speed. Math. Res. Lett., 21(5):1199–1214, 2014. doi arXiv
• L.O. Inverse obstacle problem for the non-stationary wave equation with an unknown background. Comm. Partial Differential Equations, 38(9):1492–1518, 2013. doi arXiv
• L.O. Solving an inverse obstacle problem for the wave equation by using the boundary control method. Inverse Problems, 29(3):035004, 12, 2013. doi arXiv
• T. Helin, M. Lassas, and L.O. An inverse problem for the wave equation with one measurement and the pseudorandom source. Anal. PDE, 5(5):887–912, 2012. doi arXiv
• L.O. Solving an inverse problem for the wave equation by using a minimization algorithm and time-reversed measurements. Inverse Probl. Imaging, 5(3):731–744, 2011. doi arXiv
• M. Lassas and L.O. An inverse problem for a wave equation with sources and observations on disjoint sets. Inverse Problems, 26(8):085012, 19, 2010. doi arXiv