Publications

Preprints

  1. Two Approximation Results for Divergence Free Vector Fields (with Jesse Goodman and Felipe Hernandez).
  2. On Korn-Maxwell-Sobolev Inequalities (with Franz Gmeineder).
  3. Fractional Integration and Optimal Estimates for Elliptic Systems (with Felipe Hernandez).

Refereed Journal Articles

  1. BMO and Elasticity: Korn's Inequality; Local Uniqueness in Tension (with Scott J. Spector), to appear in the Journal of Elasticity.
  2. Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers (with Scott J. Spector), to appear in Quarterly of Applied Mathematics.
  3. On the dimensional weak-type (1,1) bound for Riesz transforms (with Cody B. Stockdale), to appear in Communications in Contemporary Mathematics.
  4. An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces (with Ángel D. Martínez), Adv. Nonlinear Anal. 10 (2021), no. 1, 877–894, DOI.
  5. Some remarks on \(L^1\) embeddings in the subelliptic setting (with Steven G. Krantz and Marco Peloso), Nonlinear Anal. 202 (2021), 112149, DOI.
  6. An Optimal Sobolev Embedding for \(L^1\). J. Funct. Anal. 279 (2020), no. 3, 108559, 26 pp, DOI.
  7. A boxing inequality for the fractional perimeter (with Augusto C. Ponce). Ann. Sc. Norm. Super. Pisa Cl. Sci. 20 (2020), no. 1, 107–141, DOI.
  8. A decomposition by non-negative functions in the Sobolev space \(W^{k,1}\) (with Augusto C. Ponce). Indiana Univ. Math. J. 69 (2020), no. 1, 151–169, DOI.
  9. New directions in harmonic analysis on \(L^1\). Nonlinear Anal. 192 (2020), 111685, 20 pp., DOI.
  10. A noninequality for the fractional gradient. Port. Math 76 (2019), no. 2, 153–168,DOI.
  11. A note on estimates for elliptic systems with \(L^1\) data (with Bogdan Raiţă). C. R. Math. Acad. Sci. Paris 357 (2019), no. 11-12, 851–857, DOI.
  12. Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma (with Jean Van Schaftingen). Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), 413–436, DOI.
  13. Uniqueness of Equilibrium with Sufficiently Small Strains in Finite Elasticity (with Scott J. Spector). Arch. Ration. Mech. Anal. 233 (2019), 409–449, DOI.
  14. Best constants for two families of higher order critical Sobolev embeddings (with Itai Shafrir). Nonlinear Anal. 177 (2018), 753–769, DOI.
  15. On a new class of fractional partial differential equations II (with Tien-Tsan Shieh). Adv. Calc. Var. 11 (2018), no. 3, 289–307, DOI.
  16. Some remarks on boundary operators of Bessel extensions (with Jesse Goodman). Discrete Contin. Dyn. Syst. Ser. S  11 (2018), no. 3, 493–509, DOI.
  17. Regularity for a fractional p-Laplace equation (with Armin Schikorra and Tien-Tsan Shieh). Commun. Contemp. Math. 20 (2018), no. 1, 1750003, DOI.
  18. A remark on an integral characterization of the dual of BV (with Nicola Fusco). J. Math. Anal. Appl. 457 (2018), no. 2, 1370–1375, DOI.
  19. A note on the fractional perimeter and interpolation (with Augusto C. Ponce). C. R. Math. Acad. Sci. Paris  355 (2017), no. 9, 960–965, DOI.
  20. An \(L^1\)-type estimate for Riesz potentials (with Armin Schikorra and Jean Van Schaftingen). Rev. Mat. Iberoam. 33 (2017), no. 1, 291–303, DOI.
  21. On formulae decoupling the total variation of BV functions (with Augusto C. Ponce). Nonlinear Anal. 154 (2017), 241–257, DOI.
  22. On a generalization of Lp-differentiability Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 62, 21 pp, DOI.
  23. On the role of Riesz potentials in Poisson's equation and Sobolev embeddings (with Rahul Garg). Indiana Univ. Math. J. 64 (2015), no. 6, 1697–1719, DOI.
  24. Lp theory for fractional gradient PDE with VMO coefficients (with Armin Schikorra and Tien Tsan Shieh). Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), no. 4, 433–443, DOI.
  25. Analysis and Application of a Nonlocal Hessian (with Jan Lellmann Konstantinos Papafitsoros Carola-Bibiane Schönlieb). SIAM J. Imaging Sci. 8 (2015), no. 4, 2161–2202, DOI.
  26. On a new class of fractional partial differential equations (with Tien-Tsan Shieh). Adv. Calc. Var. 8 (2015), no. 4, 321–336, DOI.
  27. On the regularity of solutions to Poisson's equation (with Rahul Garg). C. R. Math. Acad. Sci. Paris 353 (2015), no. 9, 819–823, DOI.
  28. A Leray-Trudinger inequality (with Georgios Psaradakis). J. Funct. Anal. 269 (2015), no. 1, 215–228, DOI.
  29. Lp-Taylor approximations characterize the Sobolev space \(W^{1,p}\). C. R. Math. Acad. Sci. Paris 353 (2015), no. 4, 327–332, DOI.
  30. Localization of nonlocal gradients in various topologies (with Tadele Mengesha). Calc. Var. Partial Differential Equations 52 (2015), no. 1-2, 253–279, DOI.
  31. Corrigendum to "Characterization of Sobolev and BV spaces'' [J. Funct. Anal. 261 (10) (2011) 2926–2958]. (with Giovanni Leoni). J. Funct. Anal. 266 (2014), no. 2, 1106–1114, DOI.
  32. Characterization of Sobolev and BV spaces (with Giovanni Leoni). J. Funct. Anal. 261 (2011), no. 10, 2926–2958, DOI.
  33. Simple proofs of some results of Reshetnyak Proc. Amer. Math. Soc. 139 (2011), no. 5, 1681–1690, DOI.