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)
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:
18. J. Villavert. Regularity of solutions for fully nonlinear integral equations. In preparation.
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.
5. J. Villavert. Shooting with degree theory: Analysis of some weighted poly-harmonic systems. J. Differential Equations. 257 (4) (2014) 1148-1167. Some corrections. 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.