Weak solutions to quasilinear elliptic obstacle problems

Abstract

Weak solutions to quasilinear elliptic obstacle problems are generalized solutions used in the study of partial differential equations (PDEs). These problems involve finding a function that minimizes an energy functional while adhering to constraints imposed by an obstacle function. The "weak" aspect means that instead of requiring the solution to meet the equation point-by-point, it must satisfy an integral form of the equation. This form is particularly useful for functions that lack smoothness. In essence, weak solutions enable the study of complex variational inequalities where classical methods fall short. These solutions have significant implications in mathematical physics, finance, and other fields requiring nuanced analysis of dynamic systems.