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Journal of the London Mathematical Society Advance Access originally published online on April 30, 2008
Journal of the London Mathematical Society 2008 77(3):771-788; doi:10.1112/jlms/jdn019
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© 2008 London Mathematical Society

Stability of quasiminimizers of the p-Dirichlet integral with varying p on metric spaces

Outi Elina Maasalo

Institute of Mathematics
Helsinki University of Technology
PO Box 1100
FIN-02015 HUT
Finland

Anna Zatorska–Goldstein

Institute of Applied Mathematics and Mechanics
University of Warsaw
Banacha 2
PL-02-097 Warsaw
Poland
azator@mimuw.edu.pl

We prove a stability result, with respect to the varying exponent p, for a family of quasiminimizers of the p-Dirichlet energy functional on a doubling metric measure space. In addition, we prove global higher integrability for upper gradients of quasiminimizers with fixed boundary data, provided that the boundary data belong to a slightly better Newtonian space.

2000 Mathematics Subject Classification 49Q20 (primary), 31C45, 49N60 (secondary).

The second author is partially supported by MNiSW grant no 1PO3A 005 29 and by the Alexander von Humboldt Foundation.

Received April 24, 2006; revised September 3, 2007; published online April 30, 2008.


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