Free Boundary Problems in PDEs and Particle Systems

1. Introduction
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

Part I. The Basic Model

2. Introduction to Part I
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

3. The Basic Model, Definitions and Results
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

4. Regularity Properties of the Barriers
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

5. Lipschitz and L^1



L
1



Estimates
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

6. Mass Transport Inequalities
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

7. The Limit Theorems on Barriers
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

8. Brownian Motion and the Heat Equation
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

9. Existence of Optimal Sequences
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

10. Proof of the Main Theorem
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

11. The Basic Particle Model and Its Hydrodynamic Limit
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

Part II. Variants of the Basic Model

12. Introduction to Part II
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

13. Independent Walkers with Current Reservoirs
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

14. Beyond Diffusive Scaling
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

15. Other Models
Gioia Carinci, Anna Masi, Cristian Giardinà, Errico Presutti

Keywords: Mathematics, Partial Differential Equations, Statistical Physics, Dynamical Systems and Complexity, Mathematical Physics, Probability Theory and Stochastic Processes, Mathematical Methods in Physics, Engineering Thermodynamics, Heat and Mass Transfer