Special Session 89: Partial Differential Equations: Diverse Applications and Connections

On the Obstacle Problem for Nonlinear Materials via the Monotonicity Principle
Luisa Faella
University of Cassino and Southern Lazio
Italy
Co-Author(s):    Antonio Corbo Esposito, Vincenzo Mottola, Gianpaolo Piscitelli, Ravi Prakash, Antonello Tamburrino
Abstract:
In this talk, we discuss the Monotonicity Principle (MP) for nonlinear materials with piecewise growth exponents. This setting is particularly relevant for applications, as it enables the use of fast imaging methods based on the MP in problems involving multiple materials, at least one of which exhibits nonlinear behavior. The proposed framework is quite general and can accommodate a variety of practical configurations, including Superconducting (SC), Perfect Electric Conducting (PEC), and Perfect Electric Insulating (PEI) materials. A central role is played by the average Dirichlet-to-Neumann operator. We show how this approach can be extended to the more general setting.