RESEARCH INTERESTS:

Nonlinear analysis -- Partial Differential Equations -- Calculus of Variations

My Research Statement

RESEARCH PROFILES:

AMS MathSciNet

Google Scholar

Scopus

ORCID

PREPRINTS AND PUBLICATIONS:

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

15. J. Villavert and M. Zhu. Reversed Hardy-Littlewood-Sobolev inequality on the upper half space. In preparation.

14. J. Villavert. A sharp Liouville theorem for a nonlinear higher order elliptic equation. Preprint.

13. J. Villavert. A refined approach for non-negative entire solutions of $\Delta u + u^p = 0$ under subcritical Sobolev growth. Preprint.

12. 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.

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

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

8. 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.

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

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

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

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

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.