Department of Mathematics
Research Interest/Area of Expertise
Partial Differential Equations and Harmonic Analysis
I have been working on the mathematical theories of degenerate and singular elliptic or parabolic partial differential equations and the free boundary problems. This study include the existence, uniqueness, regularity and symmetric properties of a solution of a partial differential equation or a free boundary problem. These problems originate in physics and engineering and have seen application in science, engineering and economics.
Education – Degrees, Licenses, Certifications
- Ph.D. 1999, New York University
Wang, P., Regularity of free boundaries of two-phase problems for fully nonlinear elliptic equations of second order. Part 1: Lipschitz free boundaries are C1,α, Comm. Pure Appl. Math., Vol. LIII (2000), 799-810.
Lu, G. and Wang, P., Inhomogeneous Infinity Laplace Equation, Advances in Mathematics, Vol. 217, 4 (2008), 1838-1868.
Lu, G. and Wang, P., On the uniqueness of a solution of a two-phase free boundary problem, Journal of Functional Analysis, Vol.258(2010), 2817-2833.
Caffarelli, L.A. and Wang, P., A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition, Calculus of Variations and Partial Differential Equations, Vol 54, No.4 (2015), 3517-3529.