Katya Krupchyk's home page

Katya Krupchyk

Department of Mathematics
University of California, Irvine
510H Rowland Hall
Irvine, CA 92697-3875, USA

Office : 510H
Phone : (949) 824-8778
Email: katya.krupchyk" at "uci.edu

Teaching

Research interests

Inverse problems, partial differential equations, microlocal analysis, spectral theory

Seminars and conferences

Editorial

Papers and preprints

Inverse problems for semilinear Schrödinger equations at large frequency via polynomial resolvent estimates on manifolds, (with Shiqi Ma, Suman Kumar Sahoo, Mikko Salo, and Simon St-Amant), preprint. pdf
Inverse problems for third-order nonlinear perturbations of biharmonic operators, (with Sombuddha Bhattacharyya, Suman Kumar Sahoo, and Gunther Uhlmann), preprint. pdf
Fractional anisotropic Calderón problem on closed Riemannian manifolds, (with Ali Feizmohammadi, Tuhin Ghosh, and Gunther Uhlmann), preprint. pdf
A remark on inverse problems for nonlinear magnetic Schrödinger equations on complex manifolds, (with Gunther Uhlmann and Lili Yan), Proc. Amer. Math. Soc., to appear. pdf
Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds, (with Gunther Uhlmann), Anal. PDE 16 (2023), no. 8, 1825-1868. pdf
Partial data inverse problems for quasilinear conductivity equations, (with Yavar Kian and Gunther Uhlmann), Math. Ann. 385 (2023), no. 3-4, 1611-1638. pdf
Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds, (with Tony Liimatainen and Mikko Salo), Adv. Math. 403 (2022), Paper No. 108362, 43 pp. pdf
The Calderón inverse problem for isotropic quasilinear conductivities, (with Cătălin I. Cârstea, Ali Feizmohammadi, Yavar Kian, and Gunther Uhlmann), Adv. Math. 391 (2021), Paper No. 107956, 31 pp. pdf
Reconstruction in the Calderón problem on conformally transversally anisotropic manifolds, (with Ali Feizmohammadi, Lauri Oksanen, and Gunther Uhlmann), J. Funct. Anal. 281 (2021), no. 9, Paper No. 109191, 25 pp. pdf
Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities, (with Gunther Uhlmann), Math. Res. Lett. 27 (2020), no. 6, 1801-1824. pdf
A remark on partial data inverse problems for semilinear elliptic equations, (with Gunther Uhlmann), Proc. Amer. Math. Soc. 148 (2020), no. 2, 681-685. pdf
Eigenvalue bounds for non-self-adjoint Schrödinger operators with non-trapping metrics, (with Colin Guillarmou and Andrew Hassell), Anal. PDE 13 (2020), no. 6, 1633-1670. pdf
Stability estimates for partial data inverse problems for Schrödinger operators in the high frequency limit, (with Gunther Uhlmann), J. Math. Pures Appl. (9) 126 (2019), 273-291. pdf
Inverse problems for advection diffusion equations in admissible geometries, (with Gunther Uhlmann), Comm. Partial Differential Equations 43 (2018), no. 4, 585-615. pdf
Inverse problems for magnetic Schrödinger operators in transversally anisotropic geometries, (with Gunther Uhlmann), Comm. Math. Phys. 361 (2018), no. 2, 525-582. pdf
Bounds on eigenfunctions of semiclassical operators with double characteristics, (with Gunther Uhlmann), Asymptot. Anal., 106 (2018), no. 1, 25-46. pdf
From semiclassical Strichartz estimates to uniform L^p resolvent estimates on compact manifolds, (with Nicolas Burq and David Dos Santos Ferreira), Int. Math. Res. Not. IMRN 2018, no. 16, 5178-5218. pdf
Absolute continuity of the periodic Schrödinger operator in transversal geometry, (with Gunther Uhlmann), J. Eur. Math. Soc., 19 (2017), no. 2, 531-550. pdf
The Calderón problem with partial data for conductivities with 3/2 derivatives, (with Gunther Uhlmann), Comm. Math. Phys., 348 (2016), no. 1, 185-219. pdf
Inverse boundary problems for polyharmonic operators with unbounded potentials, (with Gunther Uhlmann), J. Spectr. Theory, 6 (2016), no. 1, 145-183. pdf
On L^p resolvent estimates for elliptic operators on compact manifolds, (with Gunther Uhlmann), Comm. Partial Differential Equations, 40 (2015), no. 3, 438-474. pdf
Uniqueness in an inverse boundary problem for a magnetic Schrödinger operator with a bounded magnetic potential, (with Gunther Uhlmann), Comm. Math. Phys., 327 (2014), no. 3, 993-1009. pdf
Inverse transmission problems for magnetic Schrödinger operators, Int. Math. Res. Notices, 2014 (2014), No. 1, 65-164. pdf
Inverse boundary value problems for the perturbed polyharmonic operator, (with Matti Lassas and Gunther Uhlmann), Trans. Amer. Math. Soc., 366 (2014), 95-112. pdf
An inverse problem for a hyperbolic system on a vector bundle and energy measurements, (with Matti Lassas), Math. Ann., 354 (2012), 1431-1464. pdf
Inverse problems with partial data for a magnetic Schrödinger operator in an infinite slab and on a bounded domain, (with Matti Lassas and Gunther Uhlmann), Comm. Math. Phys., 312 (2012), 87-126. pdf
Determining a first order perturbation of the biharmonic operator by partial boundary measurements, (with Matti Lassas and Gunther Uhlmann), J. Funct. Anal., 262 (2012), 1781-1801. pdf
A Borg-Levinson theorem for higher order elliptic operators, (with Lassi Päivärinta), Int. Math. Res. Notices, 2012 (2012), No. 6, 1321-1351. pdf
Transmission eigenvalues for elliptic operators, (with Michael Hitrik, Petri Ola, and Lassi Päivärinta), SIAM J. Math. Anal., 43 (2011), 2630-2639. pdf
Determining electrical and heat transfer parameters using coupled boundary measurements, (with Matti Lassas and Samuli Siltanen), SIAM J. Math. Anal., 43 (2011), 2096-2115. pdf
Inverse problems for differential forms on Riemannian manifolds with boundary, (with Matti Lassas and Gunther Uhlmann), Comm. Partial Differential Equations, 36 (2011), 1475-1509. pdf
The interior transmission problem and bounds on transmission eigenvalues, (with Michael Hitrik, Petri Ola, and Lassi Päivärinta), Math. Res. Lett., 18 (2011), no. 2, 279-293. pdf
Reconstruction of Betti numbers of manifolds for anisotropic Maxwell and Dirac systems, (with Yaroslav Kurylev and Matti Lassas), Comm. Anal. Geom., 18 (2010), no. 5, 963-985. pdf
Transmission eigenvalues for operators with constant coefficients, (with Michael Hitrik, Petri Ola, and Lassi Päivärinta), SIAM J. Math. Anal., 42 (2010), no. 6, 2965-2986. pdf
Inverse Spectral Problems on a Closed Manifold, (with Yaroslav Kurylev and Matti Lassas), Journal Math. Pures et Appl., 90 (2008), Issue 1, 42-59. pdf
Completion of Overdetermined Parabolic PDEs, (with Jukka Tuomela), J. Symbolic Comput., 43 (2008) 153-167. pdf
Compatibility Complexes for Overdetermined Boundary Problems, (with Jukka Tuomela), Gröbner Bases in Symbolic Analysis, Radon Ser. Comput. Appl. Math., 2, Walter de Gruyter, Berlin, 2007, 267-281. pdf
Generalised Elliptic Boundary Problems, (with Nikolai Tarkhanov and Jukka Tuomela), J. Differential Equations, 239 (2007), no. 2, 417-447. pdf
Elliptic Quasicomplexes in Boutet de Monvel Algebra, (with Nikolai Tarkhanov and Jukka Tuomela), J. Funct. Anal., 247 (2007), no. 1, 202-230. pdf
Shapiro-Lopatinskij Condition for Elliptic Boundary Value Problems, (with Jukka Tuomela), LMS J. Comput. Math., 9 (2006), 287-329. pdf
Overdetermined Elliptic PDEs, (with Werner Seiler and Jukka Tuomela), Found. Comp. Math., 6 (2006), No. 3, 309-351. pdf
The Construction of a Pfaffian System with Arbitrary Piecewise Continuous Characteristic Power-Law Functions, (with Nikolai Izobov), Differentsialnye Uravneniya 41 (2005), No. 2, 177-185 (in Russian); English transl. in Differential Equations 41 (2005), No. 2, 184-194. pdf
The Construction of the Linear Pfaffian System with the Arbitrary Given Degree Sets and Trivial Characteristic Sets, Memoirs on Differential Equations and Mathematical Physics 32 (2004), 147-150.
The Existence of the Linear Pfaffian System with Piecewise Continuous Characteristic Degree Functions, (with Nikolai Izobov), Memoirs on Differential Equations and Mathematical Physics 32 (2004), 143-146.
A Description of Exponent Sets of a Solution of a Pfaffian Linear System with Trivial Characteristic Sets, Differentsialnye Uravneniya 40 (2004), No. 10, 1319-1324 (in Russian); English transl. in Differential Equations 40 (2004), No. 10, 1389-1394. pdf
A Joint Description of the Boundary Degree Sets of the Solution of a Linear Pfaffian System. II., (with Nikolai Izobov), Differentsialnye Uravneniya 39 (2003), No. 4, 453-464 (in Russian); English transl. in Differential Equations 39 (2003), No. 4, 485-496. pdf
A Joint Description of the Boundary Degree Sets of the Solution of a Linear Pfaffian System. I., (with Nikolai Izobov), Differentsialnye Uravneniya 39 (2003), No. 3, 308-319 (in Russian); English transl. in Differential Equations 39 (2003), No. 3, 331-343. pdf
The Construction of the Linear Pfaffian System with the Arbitrary Given Boundary Degree sets, (with Nikolai Izobov), Memoirs on Differential Equations and Mathematical Physics 28 (2003), 152-158.
The Description of the Arbitrary Lower Boundary Degree Set of the Linear Pfaffian System Solution, (with Nikolai Izobov), Memoirs on Differential Equations and Mathematical Physics 27 (2002), 147-151.
Construction of an Arbitrary Boundary Lower Degree Set of the Solution of a Linear Pfaffian System, (with Nikolai Izobov), Differentsialnye Uravneniya 38 (2002), No. 10, 1310-1321 (in Russian); English transl. in Differential Equations 38 (2002), No. 10, 1393-1405. pdf
Necessary Properties of Boundary Degree Sets of Solutions to Linear Pfaffian Systems, (with Nikolai Izobov), Differentsialnye Uravneniya 37 (2001), No. 5, 616-627 (in Russian); English transl. in Differential Equations 37 (2001), No. 5, 647-658. pdf
Lower Characteristic Exponents of Nontrivial Solutions of Pfaffian systems, Differentsialnye Uravneniya 35 (1999), No. 7, 899-908 (in Russian); English transl. in Differential Equations 35 (1999), No. 7, 905-914.