Spring 2019: MATH 7380 - Topics in Elliptic Partial Differential Equations
Publications
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.
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.
N. C. Phuc and I. E. Verbitsky, Quasilimear and Hessian
equations of Lane-Emden type. Annals of
Mathematics 168 (2008), 859-914. Journal.
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.
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.
N. C. Phuc and I. E. Verbitsky, Singular quasilinear and
Hessian equations and inequalities.
Journal of Functional Analysis 256 (2009),
1875-1906. Journal.
N. C. Phuc, Quasilinear Riccati type equations
with super-critical exponents. Communications
in Partial Differential Equations 35
(2010), 1958-1981.
Journal.
Errartum.
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 .
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.
N. Garofalo and N. C. Phuc, Boundary behavior of
p-harmonic functions in the Heisenberg group.
Mathematische Annalen 351 (2011), 587-632.
Journal.
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.
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.
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.
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.
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.
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.
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.
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.
N. C. Phuc, The Navier-Stokes equations in
nonendpoint borderline Lorentz spaces. Journal
of Mathematical Fluid Mechanics 17 (2015),
741-760.
Preprint. Journal.
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.
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.
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.
N. C. Phuc, A sublinear Sobolev inequality for
p-superharmonic functions. Proceedings
of the American Mathematical Society 145
(2017), 327-334.
Preprint.
Journal.
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.
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.
K. Adimurthi, T. Mengesha, and N. C. Phuc, Gradient
weighted norm inequalities for linear elliptic
equations with discontinuous coefficients.
To appear in Applied Mathematics and Optimization.
arXiv. Journal. Remark: This paper was withdrawn from Differential and Integral Equations due to a publication fee
imposed several months after the paper had been accepted there!.
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.
K. Adimurthi and N.
C. Phuc, Nonlinear equations with gradient natural growth and distributional
data, with applications to a Schrodinger type equation. To appear in Journal of the London Mathemaical Society. arXiv.
Quoc-Hung Nguyen and N.
C. Phuc, Good-$\lambda$ and Muckenhoupt-Wheeden type bounds in quasilinear measure
datum problems, with applications. To appear in Mathematische Annalen. arXiv.
Quoc-Hung Nguyen and N.
C. Phuc, Pointwise gradient estimates for a class of singular quasilinear equation with measure data. Submitted. arXiv.