SUPERMINIMIZERS FOR ENERGY INTEGRALS IN ORLICZ-SOBOLEV SPAC-ES ON METRIC SPACES

  • MARCELINA MOCANU
    Department of Mathematics and Informatics, Faculty of Sciences, "Vasile Alecsandri" University of Bacău, 157 Calea Mărășești, 600115 Bacău, ROMANIA,

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