Professor Patricia Bauman
Professor Emerita
7654941944
MATH 439
Research Interests
 calculus of variations,
 partial differential equations,
 applied mathematics,
 materials science
My research provides rigorous investigations of the behavior of solutions to systems of partial differential equations that arise in applications of interest. My recent research is on the properties of solutions to systems of nonlinear partial differential equations and energy minimizers for mathematical models developed by physicists to describe liquid crystals and superconductors. In these materials, a rigorous description of the nature of defects is of particular interest.
Publications listed in MathSciNet
(See the CV (PDF) for all publications.)

Bauman, Patricia; Phillips, Daniel. Regularity of minimizers for a general class of constrained energies in twodimensional domains with applications to liquid crystals. Assoc. Women Math. Ser., 31. Springer, Cham, 2022, 59–78.

Bauman, Patricia; Peng, Guanying. Analysis of minimizers of the LawrenceDoniach energy for superconductors in applied fields. Discrete Contin. Dyn. Syst. Ser. B 24 (2019), no. 11, 5903–5926.

Bauman, Patricia; Phillips, Daniel; Wang, Changyou. Higher dimensional GinzburgLandau equations under weak anchoring boundary conditions. J. Funct. Anal. 276 (2019), no. 2, 447–495.

Bauman, Patricia; Phillips, Daniel. Regularity and the behavior of eigenvalues for minimizers of a constrained Qtensor energy for liquid crystals. Calc. Var. Partial Differential Equations 55 (2016), no. 4, Art. 81, 22 pp.

Bauman, Patricia; Rubiano, Andrea C. Energyminimizing nematic elastomers. Discrete Contin. Dyn. Syst. Ser. S 8 (2015), no. 2, 259–282.

Bauman, Patricia; Phillips, Daniel; Park, Jinhae. Existence of solutions to boundary value problems for smectic liquid crystals. Discrete Contin. Dyn. Syst. Ser. S 8 (2015), no. 2, 243–257.

Bauman, Patricia; Park, Jinhae; Phillips, Daniel. Analysis of nematic liquid crystals with disclination lines. Arch. Ration. Mech. Anal. 205 (2012), no. 3, 795–826.

Bauman, Patricia; Phillips, Daniel. Analysis and stability of bentcore liquid crystal fibers. Discrete Contin. Dyn. Syst. Ser. B 17 (2012), no. 6, 1707–1728.

Bauman, Patricia; Ko, Yangsuk. Analysis of solutions to the LawrenceDoniach system for layered superconductors. SIAM J. Math. Anal. 37 (2005), no. 3, 914–940.

Bauman, Patricia; Jadallah, Hala; Phillips, Daniel. Classical solutions to the timedependent GinzburgLandau equations for a bounded superconducting body in a vacuum. J. Math. Phys. 46 (2005), no. 9, 095104, 25 pp.

Andre, Nelly; Bauman, Patricia; Phillips, Dan. Vortex pinning with bounded fields for the GinzburgLandau equation. Ann. Inst. H. Poincaré C Anal. Non Linéaire 20 (2003), no. 4, 705–729.

Bauman, P.; Phillips, D.; Shen, Q. Singular limits in polymerstabilized liquid crystals. Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), no. 1, 11–34.

Bauman, Patricia; Calderer, M. Carme; Liu, Chun; Phillips, Daniel. The phase transition between chiral nematic and smectic A∗ liquid crystals. Arch. Ration. Mech. Anal. 165 (2002), no. 2, 161–186.

Bauman, Patricia; Marini, Antonella; Nesi, Vincenzo. Univalent solutions of an elliptic system of partial differential equations arising in homogenization. Indiana Univ. Math. J. 50 (2001), no. 2, 747–757.

Bauman, P.; Friesen, M.; Phillips, D. On the periodic behavior of solutions to a diffusion problem describing currents in a hightemperature superconductor. Phys. D 137 (2000), no. 12, 172–191.

Bauman, P.; Phillips, D.; Tang, Q. Stable nucleation for the GinzburgLandau system with an applied magnetic field. Arch. Rational Mech. Anal. 142 (1998), no. 1, 1–43.

Bauman, Patricia; Chen, ChaoNien; Phillips, Daniel; Sternberg, Peter. Vortex annihilation in nonlinear heat flow for GinzburgLandau systems. European J. Appl. Math. 6 (1995), no. 2, 115–126.

Bauman, Patricia; Phillips, Daniel. Univalent minimizers of polyconvex functionals in two dimensions. Arch. Rational Mech. Anal. 126 (1994), no. 2, 161–181.

Bauman, Patricia; Carlson, Neil N.; Phillips, Daniel. On the zeros of solutions to GinzburgLandau type systems. SIAM J. Math. Anal. 24 (1993), no. 5, 1283–1293.

Bauman, Patricia. Qualitative behavior of solutions to a system of partial differential equations from nonlinear elasticity. Lecture Notes in Pure and Appl. Math., 144 Marcel Dekker, Inc., New York, 1993, 53–67.

Bauman, Patricia; Owen, Nicholas C.; Phillips, Daniel. Maximum principles and a priori estimates for an incompressible material in nonlinear elasticity. Comm. Partial Differential Equations 17 (1992), no. 78, 1185–1212.

Bauman, Patricia; Phillips, Daniel; Owen, Nicholas C. Maximal smoothness of solutions to certain EulerLagrange equations from nonlinear elasticity. Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), no. 34, 241–263.

Bauman, Patricia; Owen, Nicholas C.; Phillips, Daniel. Maximum principles and a priori estimates for a class of problems from nonlinear elasticity. Ann. Inst. H. Poincaré C Anal. Non Linéaire 8 (1991), no. 2, 119–157.

Bauman, Patricia; Phillips, Daniel. A nonconvex variational problem related to change of phase. Appl. Math. Optim. 21 (1990), no. 2, 113–138.

Bauman, Patricia. Largetime behavior of solutions to a scalar conservation law in several space dimensions. Contemp. Math., 64. American Mathematical Society, Providence, RI, 1987, 209–217.

Bauman, Patricia; Phillips, Daniel. Largetime behavior of solutions to a scalar conservation law in several space dimensions. Trans. Amer. Math. Soc. 298 (1986), no. 1, 401–419.

Bauman, Patricia; Phillips, Daniel. Largetime behavior of solutions to certain quasilinear parabolic equations in several space dimensions. Proc. Amer. Math. Soc. 96 (1986), no. 2, 237–240.

Bauman, Patricia. A Wiener test for nondivergence structure, secondorder elliptic equations. Indiana Univ. Math. J. 34 (1985), no. 4, 825–844.

Bauman, Patricia. Positive solutions of elliptic equations in nondivergence form and their adjoints. Ark. Mat. 22 (1984), no. 2, 153–173.

Bauman, Patricia. Equivalence of the Green's functions for diffusion operators in Rn: a counterexample. Proc. Amer. Math. Soc. 91 (1984), no. 1, 64–68.

Bauman, Patricia. Properties of nonnegative solutions of secondorder elliptic equations and their adjoints. ProQuest LLC, Ann Arbor, MI, 1982, 154 pp.