Papers and preprints
“The L^{p} Neumann problem for higher order elliptic equations” (PDF file), submitted. 55 pages.
“The
W^{ −1, p} Neumann problem for higher order elliptic equations” (PDF file), submitted. 47 pages.
(with Steve Hofmann and Svitlana Mayboroda) “Nontangential estimates on layer potentials and the Neumann problem for higher order elliptic equations” (PDF file). Int. Math. Res. Not. IMRN (2020), https://doi.org/10.1093/imrn/rnaa051. 49 pages.
(with Steve Hofmann and Svitlana Mayboroda) “The Neumann problem for higher order elliptic equations with symmetric coefficients” (PDF file), Math. Ann. 371 (2018), no. 1–2. 34 pages.
(with Steve Hofmann and Svitlana Mayboroda) “Dirichlet and Neumann boundary values of solutions to higher order elliptic equations” (PDF file), Ann. Inst. Fourier (Grenoble) 69 (2019), no. 4. 42 pages.
(with Steve Hofmann and Svitlana Mayboroda) “Bounds on layer potentials with rough inputs for higher order elliptic equations” (PDF file), Proc. Lond. Math. Soc. (3) 119 (2019), no. 3. 44 pages.
“Perturbation of wellposedness for higherorder elliptic systems with rough coefficients” (PDF file). 47 pages.
“Extrapolation of well posedness for higher order elliptic systems with rough coefficients” (PDF file), submitted. 29 pages.
“Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces” (PDF file), Math. Inequal. Appl. 21 (2018), no. 3. 48 pages.
(with Steve Hofmann and Svitlana Mayboroda) “Square function estimates on layer potentials for higherorder elliptic equations” (PDF file), Math. Nachr. 290 (2017), no. 16. 62 pages.
“Layer potentials for general linear elliptic systems” (PDF file), Electron. J. Differential Equations 2017 (2017), no. 309. 23 pages.
“Gradient estimates and the fundamental solution for higherorder elliptic systems with rough coefficients” (PDF file), Manuscripta Math. 151 (2016), no. 3–4. 41 pages.
(with Svitlana Mayboroda) “Layer potentials and boundaryvalue problems for second order elliptic operators with data in Besov spaces” (PDF file), Mem. Amer. Math. Soc. 243 (2016), no. 1149. 109 pages, 17 figures. There is also a version with colored figures.
(with Svitlana Mayboroda) “Higherorder elliptic equations in nonsmooth domains: a partial survey” (PDF file),
Harmonic analysis, partial differential equations, complex analysis, Banach spaces, and operator theory. Vol. 1, 55–121, Assoc. Women Math. Ser., 4, Springer, [Cham], 2016. 56 pages. An earlier version appeared in: Concrete operators, spectral theory, operators in
harmonic analysis and approximation, Oper. Theory Adv. Appl., vol. 236,
Birkhäuser/Springer, Basel, 2014. 41 pages.
“The Dirichlet problem with BMO boundary data and almostreal coefficients” (PDF file), Rev. Mat. Iberoam. 31 (2015), no. 2. 29 pages.
(with Lesley Ward) “A new class of harmonic measure distribution functions” (PDF file), J. Geom. Anal. 24 (2014), no. 4. 34 pages, 7 figures.
(with Svitlana Mayboroda) “The Dirichlet problem for higher order equations in composition form” (PDF file). J. Funct. Anal. 265 (2013), no. 1. 51 pages.
“Elliptic partial differential equations with almostreal coefficients” (PDF file). Mem. Amer. Math. Soc. 223 (2013), no. 1051. 108 pages, 5 figures.
Documents
My curriculum vita (PDF file)
Exam timer
Direction field plotter
Phase plane plotter
