PROFESSIONAL EXPERIENCE

1. Associate Professor, University of Texas, Rio Grande Valley, Edinburg, TX, 2021-Present

2. Assistant Professor, University of Texas, Rio Grande Valley, Edinburg, TX, 2015-2020

3. Research Member, Mathematical Sciences Research Institute, Berkeley, CA, 2016

4. Visiting Assistant Professor, University of Oklahoma, Norman, OK, 2013-2015

5. NSF EAPSI Fellow, Shanghai Jiao Tong University, Shanghai, China, Summer 2012

6. PhD, University of Colorado, Boulder, CO, 2013


RESEARCH INTERESTS:

Geometric and Nonlinear Analysis -- Partial Differential Equations -- Calculus of Variations


RESEARCH PROFILES:

AMS MathSciNet (subscription required)

Google Scholar

Scopus


GRANTS, FELLOWSHIPS AND PROGRAMS

National Science Foundation, NSF EAPSI-1209513, 2012 ($6,126)

Visiting Scholar Program, Fudan University, 2019-2020

Visiting Scholar, Shanghai Jiao Tong University, 2019-

Simons Foundation, Collaboration Grants for Mathematicians, 2017-2022 ($42,000)


PREPRINTS AND PUBLICATIONS:

20. H. Ansari and J. Villavert. Supercritical Hardy-Sobolev inequalities and their applications. In preparation.

19. J. Villavert. Regularity of solutions for fully nonlinear integral equations. In preparation.

18. J. Villavert. Existence, proportionality and classification results for certain elliptic systems. J. Math. Anal. Appl., No. 2, Paper no. 129328, 2025.

17. J. Villavert. Existence and non-existence results for cooperative elliptic systems without variational structure. NoDEA Nonlinear Differential Equations and Appl., No. 1, Paper No. 12, 19pp, 2024.

16. J. Villavert. On problems with weighted elliptic operator and general growth nonlinearities. Commun. Pure Appl. Anal., 20 (4) (2021) 1347-1361.

15. J. Villavert. Classification of radial solutions to equations related to Caffarelli-Kohn-Nirenberg inequalities. Ann. Mat. Pura Appl., 199 (1) (2020) 299-315.

14. J. Villavert. A refined approach for non-negative entire solutions of $\Delta u + u^p = 0$ under subcritical Sobolev growth. Adv. Nonlinear Stud. 17 (4) (2017) 691-703.

13. C. Li and J. Villavert. Existence of positive solutions to semilinear elliptic systems with supercritical growth. Comm. Partial Differential Equations. 41 (7) (2016) 1029-1039.

12. C. Li and J. Villavert. A degree theory framework for semilinear elliptic systems. Proc. Amer. Math. Soc. 144 (9) (2016) 3731-3740.

11. J. Dou, F. Ren and J. Villavert. Classification of positive solutions to a Lane-Emden type integral system with negative exponents. Discrete Contin. Dyn. Syst. 36 (12) (2016) 6767-6780.

10. J. Villavert. Asymptotic and optimal Liouville properties for Wolff type integral systems. Nonlinear Anal. 130 (2016) 102-120.

9. J. Villavert. A characterization of fast decaying solutions for quasilinear and Wolff type systems with singular coefficients. J. Math. Anal. Appl. 424(2) (2015) 1348-1373.

8. J. Villavert. Qualitative properties of solutions for an integral system related to the Hardy-Sobolev inequality. J. Differential Equations. 258(5) (2015) 1685-1714.

7. J. Villavert. Sharp existence criteria for positive solutions of Hardy-Sobolev type systems. Commun. Pure Appl. Anal. 14 (2) (2015) 493-515.

6. C. Deng and J. Villavert. Ill-posedness of the two-dimensional Keller-Segel model in Triebel-Lizorkin spaces. Nonlinear Anal. 95 (2014) 38-49.

5. J. Villavert. Shooting with degree theory: Analysis of some weighted poly-harmonic systems. J. Differential Equations. 257 (4) (2014) 1148-1167. Some corrections.

4. J. Villavert. The Analysis of Some Nonlinear Partial Differential Equations. PhD Dissertation. University of Colorado (2013) 1-113.

3. J. Villavert and K. Mohseni. An inviscid regularization of hyperbolic conservation laws. J. Appl. Math. Comput. 43 (1-2) (2013) 55-73.

2. C. Li and J. Villavert. An extension of the Hardy-Littlewood-Pòlya inequality. Acta. Math. Sci. 31B (6) (2011) 2285-2288.

1. J. Villavert and K. Mohseni. A regularization of the Burgers-Continuity equations using high wavenumber filtering. 40th Fluid Dynamics Conference and Exhibit, AIAA-2010-4469, Chicago, IL, 2010.


LECTURE NOTES:

1. Elementary theory and methods for elliptic partial differential equations.

2. The incompressible Euler and Navier-Stokes equations.

3. A primer on measure theory and Radon measures.

4. MATH 5390 Final Lectures on Riemann Integration Notes.