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Nguyen Cong Phuc, Professor

Office: 312 Lockett Hall Phone: (225) 578-1581 Email: [email protected]

Research Interests

Partial Differential Equations, Harmonic Analysis, and Nonlinear Potential Theory.

Teaching

Spring 2025: MATH 7375 Wavelets

Publications

    1. N. C. Phuc and I. E. Verbitsky, Local integral estimates and removable singularities for quasilinear and Hessian equations with nonlinear source terms. Communications in Partial Differential Equations 31 (2006), 1779-1791. Journal.

    2. D. M. Duc, N. C. Phuc and T. V. Nguyen, Weighted Sobolev's inequalities for bounded domains and singular elliptic equations. Indiana University Mathematics Journal 56 (2007), 615-642. Journal.

    3. N. C. Phuc and I. E. Verbitsky, Quasilimear and Hessian equations of Lane-Emden type. Annals of Mathematics 168 (2008), 859-914. Journal.

    4. N. C. Phuc and M. Torres, Characterizations of the existence and removable singularities of divergence-measure vector fields. Indiana University Mathematics Journal 57 (2008), 1573-1598. Journal.

    5. D. Danielli, N. Garofalo and N. C. Phuc, Inequalities of Hardy-Sobolev type in Carnot-Caratheodory spaces. Sobolev Spaces in Mathematics I. Sobolev Type Inequalities. Vladimir Maz'ya Ed. International Mathematical Series 8 (2009), 117-151. arXiv. Springer.

    6. N. C. Phuc and I. E. Verbitsky, Singular quasilinear and Hessian equations and inequalities. Journal of Functional Analysis 256 (2009), 1875-1906. Journal.

    7. N. C. Phuc, Quasilinear Riccati type equations with super-critical exponents. Communications in Partial Differential Equations 35 (2010), 1958-1981. Journal. Errartum.

    8. N. C. Phuc, Weighted estimates for nonhomogeneous quasilinear equations with discontinuous coefficients. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5). Vol. X (2011), 1-17. Journal .

    9. D. Danielli, N. Garofalo and N. C. Phuc, Hardy-Sobolev type inequalities with sharp constants in Carnot-Caratheodory spaces. Potential Analysis 34 (2011), 223-242. Journal.

    10. N. Garofalo and N. C. Phuc, Boundary behavior of p-harmonic functions in the Heisenberg group. Mathematische Annalen 351 (2011), 587-632. Journal.

    11. T. Mengesha and N. C. Phuc, Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains. Journal of Differential Equations 250 (2011), 1485-2507. Journal.

    12. T. Mengesha and N. C. Phuc, Global estimates for quasilinear elliptic equations on Reifenberg flat domains. Archive for Rational Mechanics and Analysis 203 (2012), 189-216. Journal.

    13. N. C. Phuc, On Calderon-Zygmund theory for p- and A-superharmonic functions. Calculus of Variations and Partial Differential Equations 46 (2013) 165-181. Journal.

    14. T. V. Phan and N. C. Phuc, Stationary Navier-Stokes equations with critically singular external forces: existence and stability results. Advances in Mathematics 241 (2013), 137-161. Preprint. Journal.

    15. N. C. Phuc and I. E. Verbitsky, Quasilinear equations with source terms on Carnot groups. Trans. Amer. Math. Soc. 365 (2013), 6569-6593. Preprint. Journal.

    16. N. C. Phuc, Global integral gradient bounds for quasilinear equations below or near the natural exponent. Arkiv for Matematik 52 (2014), 329-354. Preprint. Journal.

    17. N. C. Phuc, Morrey global bounds and quasilinear Riccati type equations below the natural exponent. Journal de Mathématiques Pures et Appliquées 102 (2014), 99-123. Preprint. Journal.

    18. N. C. Phuc, Nonlinear Muckenhoupt-Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations. Advances in Mathematics 250 (2014), 387-419. Preprint. Journal. Corrigendum.

    19. K. Adimurthi and N. C. Phuc, Global Lorentz and Lorentz-Morrey estimates below the natural exponent for quasilinear equations. Calculus of Variations and Partial Differential Equations 54 (2015), 3107-3139. Preprint. Journal.

    20. N. C. Phuc, The Navier-Stokes equations in nonendpoint borderline Lorentz spaces. Journal of Mathematical Fluid Mechanics 17 (2015), 741-760. Preprint. Journal.

    21. T. Mengesha and N. C. Phuc, Quasilinear Riccati type equations with distributional data in Morrey space framework. Journal of Differential Equations 260 (2016), 5421-5449. Preprint. Journal.

    22. K. Adimurthi and N. C. Phuc, An end-point global gradient weighted estimate for quasilinear equations in non-smooth domains. Manuscripta Mathematica 150 (2016), 111-135. Preprint. Journal.

    23. N. C. Phuc and M. Torres, Characterizations of signed measures in the dual of BV and related isometric isomorphisms. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5). Vol. XVII (2017) 385-417. Preprint.

    24. N. C. Phuc, A sublinear Sobolev inequality for p-superharmonic functions. Proceedings of the American Mathematical Society 145 (2017), 327-334. Preprint. Journal.

    25. C. Guevara and N. C. Phuc, Local energy bounds and $\epsilon$-regularity criteria for the 3D Navier-Stokes system. Calculus of Variations and Partial Differential Equations 56 (2017), 1-16. Preprint. Journal.

    26. C. Guevara and N. C. Phuc, Leray's self-similar solutions to the Navier-Stokes equations with profiles in Marcinkiewicz and Morrey spaces. SIAM Journal on Mathematical Analysis 50 (2018), 541-556. Preprint. Journal.

    27. K. Adimurthi and Cong Phuc Nguyen, Quasilinear equations with natural growth in the gradients in spaces of Sobolev multipliers. Calculus of Variations and Partial Differential Equations 57 (2018), Art. 74, 23 pp. arXiv. Journal.

    28. K. Adimurthi and N. C. Phuc, Nonlinear equations with gradient natural growth and distributional data, with applications to a Schrodinger type equation. Journal of the London Mathemaical Society 98 (2018), 461-482. arXiv. Journal.

    29. Q.-H. Nguyen and N. C. Phuc, Good-$\lambda$ and Muckenhoupt-Wheeden type bounds in quasilinear measure datum problems, with applications. Mathematische Annalen 374 (2019), 67-98. arXiv. Journal.

    30. Q.-H. Nguyen and N. C. Phuc, Pointwise gradient estimates for a class of singular quasilinear equation with measure data. Journal of Functional Analysis 278 (2020), no. 5, 108391, 35 pp. arXiv. Journal.

    31. Q.-H. Nguyen and N. C. Phuc, Quasilinear Riccati type equations with oscillatory and singular data. Advanced Nonlinear Studies 20 (2020), 373-384. arXiv. Journal.

    32. K. Adimurthi, T. Mengesha, and N. C. Phuc, Gradient weighted norm inequalities for linear elliptic equations with discontinuous coefficients. Applied Mathematics and Optimization 83 (2021), 327-371. arXiv. Journal.

    33. Q.-H. Nguyen and N. C. Phuc, Existence and regularity estimates for quasilinear equations with measure data: the case 1 < p <= (3n-2)/(2n-1). Analysis & PDE 15 (2022), No. 8, 1879-1895. Available at arXiv.

    34. N. C. Phuc and Igor E. Verbitsky, BMO solutions to quasilinear equations of p-Laplace type. Annales de l'institut Fourier (Grenoble) 72 (2022), no. 5, 1911–1939. Available at arXiv.

    35. K. H. Ooi and N. C. Phuc, Characterizations of predual spaces to a class of Sobolev multiplier type spaces. Journal of Functional Analysis 282 (2022), no. 6, Paper No. 109348, 52 pp. Available at arXiv.

    36. K. H. Ooi and N. C. Phuc, On a capacitary strong type inequality and related capacitary estimates. Revista Matemática Iberoamericana 38 (2022), no. 2, 589-599. Available at arXiv.

    37. K. H. Ooi and N. C. Phuc, The Hardy-Littlewood maximal function, Choquet integrals, and embeddings of Sobolev type. Mathematische Annalen 382 (2022), no. 3-4, 1865-1879.

    38. Q.-H. Nguyen and N. C. Phuc, Universal potential estimates for 1< p <=2-1/n. Mathematics in Engineering 5 (2023), no. 3, Paper No. 057, 24 pp. Available at arXiv.

    39. N. C. Phuc and Igor E. Verbitsky, Uniqueness of entire solutions to quasilinear equations of p-Laplace type. Mathematics in Engineering 5 (2023), no. 3, Paper No. 068, 33 pp. Available at arXiv.

    40. N. C. Phuc, The spherical maximal function on Choquet spaces. Acta Mathematica Vietnamica (2022). https://doi.org/10.1007/s40306-022-00488-9

    41. Q.-H. Nguyen and N. C. Phuc, A comparison estimate for singular p-Laplace equations and its consequences. Arch Rational Mech Anal 247, 49 (2023). https://doi.org/10.1007/s00205-023-01884-7. Also available at arXiv.

    42. N. C. Phuc and K. H. Ooi, Some capacitary strong type inequalities and related function spaces. Submitted for publication, preprint 2024.

    43. S.-K. Chua and N. C. Phuc, Inequalities of Poincare and Sobolev type for A-superharmonic functions. Submitted for publication, preprint 2024.

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