Russell Brown Mathematics Arts and Sciences University of Kentucky

Recent publications

Brascamp-Lieb-forms Scattering theory Boundary value problems Inverse problems

Scattering theory

  • An estimate arising in scattering theory arXiv
  • Appendix to: Soliton solutions and their (in)stability for the focusing Davey-Stewartson II equation by Peter Perry, Nonlinearity, 31 (2018), 4290-4325. arXiv | doi
  • Action of a scattering map on weighted Sobolev spaces in the plane, with P.A. Perry, K.A. Ott and with an appendix co-authored by N. Serpico, J. Funct. Anal., 271 (2016), 85-106. arXiv | doi
  • Estimates for a scattering map associated to a two-dimensional first order system, J. Nonlinear Sci. (2001) arXiv | doi

Brascamp-Lieb forms

  • Estimates for Brascamp-Lieb forms in \(L^p\) spaces with power weights, with C.W. Lee and K.A. Ott, Proc. Amer. Math. Soc., 149 (2021), 747-760. arXiv | doi
  • Estimates for a family of multi-linear forms, with Z. Nie, Journal of Mathematical Analysis and Applications, 377 (2011), 79-87. arXiv | doi

Boundary value problems

  • Extendability of functions with partially vanishing trace. with Robert Haller-Dintelmann and Patrick Tolksdorf, arXiv
  • Estimates for the \(L^q\)-mixed problem in \(C^{1,1}\)-domains, with L.D. Croyle, Complex variables and elliptic equations 66 (2021), 181-193. arXiv | doi
  • The Green function for the mixed problem for the linear Stokes system in domains in the plane, with K.A.Ott and S. Kim , Math. Nachr. 288 (2015), 452-464. arXiv | doi.
  • Heat kernel for the elliptic system of linear elasticity with boundary conditions, with J. Taylor and S. Kim , J. Differential Equations, 257 (2014), no. 7, 2485-2519, arXiv | doi
  • The mixed problem for the Lamé system in two dimensions, with K.A. Ott, J. Diff. Equations, 254 (2013), 4373-4400, arXiv | doi
  • The Green function for elliptic systems in two dimensions, with J.L. Taylor and S. Kim , Comm. PDE, 38 (2013), 1574-1600. arXiv | doi
  • The mixed problem in Lipschitz domains with general decompositions of the boundary, with J.L. Taylor and K.A. Ott, Trans. Amer. Math. Soc., 365 (2013), 2895-2930, arXiv | doi
  • The mixed problem for the Laplacian in Lipschitz domains, with K.A. Ott, Potential analysis, 38 (2013), 1333-1364, arXiv | Springerlink | doi Correction: arXiv | doi
  • Mixed boundary value problems for the Stokes system, with Irina Mitrea, Marius Mitrea and Matt Wright, Trans. Amer. Math. Soc., 362 (2010), 1211-1230. pdf | doi
  • The mixed problem for the Lamé system in a class of Lipschitz domains, with Irina Mitrea, J. Differential Equations 246 (2009), 2577-2589, pdf | doi
  • The mixed problem in \(L^p\) for some two-dimensional Lipschitz domains, with Loredana Lanzani and Luca Capogna, Mat. Ann. 342 (2008), 91-124, arXiv | doi
  • The Mixed Boundary Problem in \(L^p\) and Hardy spaces for Laplace's Equation on a Lipschitz Domain, with Jeffery Sykes Contemporary Math., 277 (2001), 1-18. pdf.
  • Absorbing boundary technique for open channel flows, with Scott A. Yost and Prasada Rao Int. J. Numer. Meth. Fluids, 33 (2000), 641-656.
  • Boundary value problems for higher order parabolic equations, with Wei Hu, Trans. Amer. Math. Soc. 353 pdf | Transactions
  • On the dimension of the attractor for the non-homogeneous Navier-Stokes equations in non-smooth domains with Peter Perry and Zhongwei Shen , Indiana Univ. Math. J. 49 (2000), no. 1, 81--112. pdf
  • Regularity of solutions to a contact problem with Zhongwei Shen and Peter Shi, Trans. Amer. Math. Soc. 350 (1998). 4053-4063. pdf | doi
  • The additive turbulent decomposition for the two-dimensional incompressible Navier-Stokes equations: convergence theorems and error estimates with Peter Perry and Zhongwei Shen, SIAM J. Applied Math., 59 (1999). doi
  • Weak solutions of parabolic equations in non-cylindrical domains with Wei Hu and Gary Lieberman, Proc. Amer. Math. Soc. 125 (1997), 1785-1792, pdf
  • Estimates for the Stokes operator in Lipschitz domains with Zhongwei Shen, Indiana U. Math. J., 44 (1995), 1183-1206. pdf | doi
  • The mixed problem for Laplace's equation in a class of Lipschitz domains, Comm. Partial Differential Equations 19 (1994), no. 7-8, 1217--1233, pdf | doi

Inverse problems

  • Inverse boundary value problems for polyharmonic operators with non-smooth coefficients, with L.D. Gauthier, Inverse Problems and Imaging 16(4), 943-966, , arXiv | doi
  • Appendix: Recovering the gradient of a C1-conductivity at the boundary, with A. Garcia and G. Zhang. This is an appendix to a paper by Garcia and Zhang titled Reconstruction from boundary measurements for less regular conductivities, arXiv
  • Identifiability at the boundary for first-order terms, with Mikko Salo, Applicable Analysis, 85 (2006), 735-749. pdf
  • Uniqueness in the inverse conductivity problem for conductivities with 3/2 derivatives in \(L^p, p>2n\) with Rodolfo H. Torres J. Fourier Analysis and Applications 9 (2003), 563-574, pdf.
  • Recovering the conductivity at the boundary from the Dirichlet to Neumann map: a pointwise result, J. inverse and ill-posed prob. 9 (2001). pdf
  • Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions, with Gunther Uhlmann, Comm. Partial Differential Equations, 22 (1997), no. 5-6, 1009-1027, pdf | doi
  • The impedance imaging problem for less regular conductivities, SIAM J. Math Anal. 27 (1996), 1049-1056, pdf | doi