Publications

Refereed Journal Articles

  1.  D. Spector, Simple proofs of some results of Reshetnyak, Proc. Amer. Math. Soc. 139 (2011), 1681-1690.

  2. G. Leoni and D. Spector, Characterization of Sobolev and BV spaces, J. Funct. Anal. 261 (2011), 2926-2958.

  3. G. Leoni and D. Spector, Corrigendum to ”Characterization of Sobolev and BV spaces”, J. Funct. Anal. 266 (2014), 1106-1114.

  4. T-T. Shieh and D. Spector, On a new class of fractional partial differential equations, Adv. Calc. Var. 8 (2015), no. 4, 321-336.

  5. T. Mengesha and D. Spector, Localization of Nonlocal Gradients in Various Topologies, Calc. Var. Partial Differential Equations 52 (2015), 253-279.

  6. D. Spector, Lp-Taylor approximations characterize the Sobolev space W1,p, C. R. Math. Acad. Sci. Paris 353 (2015), 327-332.

  7. G. Psaradakis and D. Spector, A Leray-Trudinger inequality, J. Funct. Anal. 269 (2015), 215-228.

  8. R. Garg and D. Spector, On regularity of solutions to Poisson’s equation, C. R. Math. Acad. Sci. Paris 353 (2015), 819-823.

  9. J. Lellmann, K. Papafitsoros, C. Schonlieb and D. Spector, Analysis and Application of a Nonlocal Hessian, SIAM J. Imaging Sci. 8 (2015), no. 4, 2161-2202.

  10. A. Schikorra, T.-T. Shieh, and D. Spector, Lp theory for fractional gradient PDEs with VMO coefficients, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), 433-443.

  11. R. Garg and D. Spector, On the role of Riesz potentials in Poisson’s equation and Sobolev embeddings,  Indiana U Math J. 64 (2015), no. 6, 1697-1719.

  12. D. Spector, On a generalization of Lp-differentiability, Calc. Var. Partial Differential Equations 55  (2016), no. 3, 55:62.

  13. A. Schikorra, D. Spector, and J. Van Schaftingen, An L1-type estimate for Riesz potentials, Rev. Mat. Iberoam. 33 (2017), no. 1, 291-304.

  14. A. Ponce and D. Spector, On formulae decoupling the total variation of BV functions, Nonlinear Anal. 154 (2017), 241-257.

  15. A. Ponce and D. Spector, A note on the Fractional Perimeter and Interpolation, C. R. Math. Acad. Sci. Paris 355 (2017), no. 9, 960-965.

  16. A. Schikorra, T-T. Shieh and D. Spector, Regularity for a fractional p-Laplace’s equation, Commun. Contemp. Math. 20 (2018), no. 1, 1750003, 6 pp.

  17. N. Fusco and D. Spector, A Remark on an Integral Characterization of the Dual of BV, J. Math.  Anal. Appl. 457 (2018), no. 2, 1370-1375.

  18. J. Goodman and D. Spector, Some remarks on boundary operators of Bessel extensions, Discrete Contin. Dyn. Syst. Ser. S 11 (2018), no. 3, p. 493-509.

  19. T-T. Shieh and D. Spector, On a new class of fractional partial differential equations II, Adv. Calc. Var. 11 (2018), no. 3, 289-307.

  20. I. Shafrir and D. Spector, Best constants for two families of higher order Sobolev embeddings, Nonlinear Anal. 177 (2018), part B, 753-769.

  21. D. Spector and S. Spector, Uniqueness of Equilibrium with sufficiently small strains in Finite Elasticity, Arch. Rational Mech. Anal. 233 (2019), 409-449.

  22. D. Spector and J. Van Schaftingen, Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo’s lemma, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019),  no. 3, 413-436.

  23. D. Spector, New Directions in Harmonic Analysis on L1, Nonlinear Anal. 192 (2020), 111685.
     
  24. B. Rait, ̆a and D. Spector, A Note on Estimates for Elliptic Systems with LDataC. R. Math. Acad. Sci. Paris (2019), no. 11-12, 851-857.
     
  25. A. Ponce and D. Spector, A Boxing Inequality for the Fractional Perimeter, Ann. Scuola Norm. Sup. Pisa Cl. Sci (5).  20 (2020), no. 1, 1-35.
     
  26. A. Ponce and D. Spector, A decomposition by non-negative functions in the Sobolev space Wk,1,  Indiana U Math J. (to appear), https://www.iumj.indiana.edu/IUMJ/forthcoming.php.
     
  27. D. Spector, A Noninequality for the Fractional Gradient, Portugal. Math. (to appear).

Preprints

  1. D. Spector, An Optimal Sobolev Embedding for L1, preprint, arXiv:1806.07588.
     
  2. S. Krantz, M. Peloso, and D. Spector, Some remarks on L1 embeddings in the subelliptic setting, preprint, arXiv:1906.01896.