Abstract
We extend the basic part of the study of superminimizers for Dirichlet energy integrals on metric spaces, initiated in a seminal paper by J. Kinnunen and O. Martio (2002) and thor-oughly undertaken in the monograph of A. Bjorn and J. Bjorn (2011), to a case where the role of Newtonian spaces is played by more general Orlicz-Sobolev spaces. We prove a comparison principle for obstacle problems in this generalized setting, then we give some characterizations of superminimizers and methods of constructing new supermini-mizers from existing ones. Finally, we establish a two-way connection
between the solutions of obstacle problems and the superminimizers associated to an en-ergy integral.
Cuvinte cheie
doubling metric measure space
Orlicz-Sobolev space
variational integral
obstacle prob-lem
superminimizer