Issue:

SSRSMI, Number 2, Volume XXVII

Section:

Volume 27, Number 2

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.

Keywords:

doubling metric measure space, Orlicz-Sobolev space, variational integral, obstacle prob-lem, superminimizer.

Code [ID]:

SSRSMI201702V27S01A0010 [0004752]

Note:

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