We define a Thomas-Fermi-von Weizsäcker model for polymers and thin films through a thermodynamic limit process. Our argument makes use of standard techniques for elliptic PDEs, such as maximum principles or supersolution methods. In the course of our work, we establish some existence and uniqueness results for a system of nonlinear PDEs.
"Thomas-Fermi type theories for polymers and thin films." Adv. Differential Equations 5 (7-9) 977 - 1032, 2000.