司靈得 (Daniel Spector)

  • Research
  • Publications
  • Teaching
  • Seminar
  • Video Library
  • Education

Preprints

  1. Constrained differential operators, Sobolev inequalities, and Riesz potentials (with Dominic Breit, and Andrea Cianchi)
  2. Math Display On the Trace of \(\dot{W}_a^{m+1,1}(\mathbb{R}^{n+1}_+)\) (with Giovanni Leoni)
  3. On dimension stable spaces of measures (with Dmitriy Stolyarov)
  4. Potential trace inequalities via a Calderón-type theorem (with Zdeněk Mihula, and Luboš Pick )
  5. Math Display \(BMO\) and gradient estimates for solutions of critical elliptic equations (with You-Wei Benson Chen, and Juan Manfredi)
  6. A sparse resolution of the DiPerna-Majda gap problem for 2D Euler equations (with Oscar Domínguez)
  7. On sharp constants in higher order Adams-Cianchi inequalities (with Prasun Roychowdhury)
Refereed Journal Articles
  1. On functions of bounded β-dimensional mean oscillation (with You-Wei Chen) Advances in Calculus of Variations 17 (2024), no. 3. DOI.
  2. Two Approximation Results for Divergence Free Vector Fields (with Jesse Goodman and Felipe Hernandez) Portugaliae Mathematica 81 (2024), no.3-4. DOI.
  3. Fractional Integration and Optimal Estimates for Elliptic Systems (with Felipe Hernandez) Calculus of Variations and Partial Differential Equations 63 (2024), no. 5, Paper No. 117. DOI.
  4. Capacitary Maximal Inequalities and Applications (with You-Wei Benson Chen and Keng Hao Ooi) Journal of Functional Analysis 286.12 (2024): 110396. DOI.
  5. Some Remarks on Capacitary Integrals and Measure Theory (with Augusto Ponce) arXiv:2302.11847v1 [math.FA] (2023). DOI.
  6. On functions of bounded β-dimensional mean oscillation (with You-Wei Benson Chen) arXiv:2207.06979v2 [math.AP] (2022). DOI.
  7. On Korn’s First Inequality in a Hardy-Sobolev Space (with Scott J. Spector) Journal of Elasticity (2023), 1-12. DOI.
  8. A trace inequality for solenoidal charges (with Bogdan Raiţă and Dmitry Stolyarov) Potential Analysis 59.4 (2023): 2093-2104.  DOI.
  9. Math Display The fractional variation and the precise representative of \(BV^{\alpha,p}\) functions (with Giovanni E. Comi and Giorgio Stefani) Fract. Calc. Appl. Anal. 25, 520-558 (2022). DOI.
  10. Math Display Endpoint \(L^1\) estimates for Hodge systems(with Felipe Hernandez and Bogdan Raiţă)  Math. Ann. (2022). DOI.
  11. Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers (with Scott J. Spector) Quart. Appl. Math. 79 (2021), no. 3, 409–417. DOI.
  12. On the dimensional weak-type (1,1) bound for Riesz transforms (with Cody B. Stockdale) Commun. Contemp. Math. 23 (2021), no. 7, Paper No. 2050072, 19 pp. DOI.
  13. On Korn-Maxwell-Sobolev Inequalities (with Franz Gmeineder) J. Math. Anal. Appl. 502 (2021), no. 1, 125226, DOI.
  14. BMO and Elasticity: Korn's Inequality; Local Uniqueness in Tension (with Scott J. Spector) J. Elasticity 143 (2021), no. 1, 85-109, DOI.
  15. 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.
  16. Math Display Some remarks on \(L^1\) embeddings in the subelliptic setting (with Steven G. Krantz and Marco Peloso) Nonlinear Anal. 202 (2021), 112149, DOI.
  17. Math Display An Optimal Sobolev Embedding for \(L^1\) J. Funct. Anal. 279 (2020), no. 3, 108559, 26 pp, DOI.
  18. 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.
  19. Math Display 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.
  20. Math Display New Directions in Harmonic Analysis on \(L^1\) Nonlinear Anal 192 (2020), 111685, 20 pp., DOI.
  21. A Noninequality for the Fractional Gradient Port. Math 76 (2019), no. 2, 153–168,DOI.
  22. Math Display 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.
  23. 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.
  24. Uniqueness of Equilibrium with Sufficiently Small Strains in Finite Elasticity (with Scott J. Spector) Arch. Ration. Mech. Anal. 233 (2019), 409–449, DOI.
  25. Best constants for two families of higher order critical Sobolev embeddings (with Itai Shafrir) Nonlinear Anal. 177 (2018), 753–769, DOI.
  26. On a new class of fractional partial differential equations II (with Tien-Tsan Shieh) Adv. Calc. Var. 11 (2018), no. 3, 289–307, DOI.
  27. Some remarks on boundary operators of Bessel extensions (with Jesse Goodman) Discrete Contin. Dyn. Syst. Ser. S  11 (2018), no. 3, 493–509, DOI.
  28. Regularity for a fractional p-Laplace equation (with Armin Schikorra and Tien-Tsan Shieh) Commun. Contemp. Math. 20 (2018), no. 1, 1750003, DOI.
  29. 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.
  30. 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.
  31. Math Display 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.
  32. On formulae decoupling the total variation of BV functions (with Augusto C. Ponce) Nonlinear Anal. 154 (2017), 241–257, DOI.
  33. Math Display On a generalization of \(L^p\)-differentiability Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 62, 21 pp, DOI.
  34. 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.
  35. Math Display \(L^p\)-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.
  36. 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.
  37. On a new class of fractional partial differential equations, part 2/2 (with Tien-Tsan Shieh) Adv. Calc. Var. 8 (2015), no. 4, 321–336, DOI.
  38. 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.
  39. A Leray-Trudinger inequality (with Georgios Psaradakis) J. Funct. Anal. 269 (2015), no. 1, 215–228, DOI.
  40. Math Display \(L^p\)-Taylor approximations characterize the Sobolev space \(W^{1,p}\)  353 (2015), no. 4, 327–332, DOI.
  41. Localization of nonlocal gradients in various topologies (with Tadele Mengesha) Calc. Var. Partial Differential Equations 52 (2015), no. 1-2, 253–279, DOI.
  42. On a new class of fractional partial differential equations, part 1/2 (with Tien-Tsan. Shieh) Adv. Cale. Var. 8 (2015), no. 4, 321-336.

  43. \(L^p\)-Taylor approximations characterize the Sobolev space \(W^{1,p}\)

     (with Giovanni Leoni) J. Funct. Anal. 266 (2014), no. 2, 1106–1114,     DOI    .
  44. Characterization of Sobolev and BV spaces (with Giovanni Leoni) J. Funct. Anal. 261 (2011), no. 10, 2926–2958, DOI.
  45. Simple proofs of some results of Reshetnyak Proc.  Amer. Math. Soc. 139 (2011), no. 5, 1681–1690, DOI.

 

Back to Top