Fall 2014, Math 112A, Introduction to partial differential equations
Research interests
Partial differential equations, inverse problems, spectral and scattering theory
Papers and preprints
Eigenvalue bounds for non-self-adjoint Schrödinger operators with non-trapping metrics, (with Colin Guillarmou and Andrew Hassell), preprint 2017, submitted. pdf
Stability estimates for partial data inverse problems for Schrödinger operators in the high frequency limit, (with Gunther Uhlmann),
J. Math. Pures Appl., to appear. pdf
Inverse problems for advection diffusion equations in admissible geometries, (with Gunther Uhlmann), Comm. Partial Differential Equations, to appear. 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
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), Differentsial’nye
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, Differentsial’nye 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), Differentsial’nye 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), Differentsial’nye 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),
Differentsial’nye
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), Differentsial’nye 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, Differentsial’nye Uravneniya 35 (1999), No. 7,
899-908 (in Russian); English transl. in Differential Equations 35
(1999), No. 7, 905-914.