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- Publisher
- Springer Journals
- Copyright
- Copyright © 2004 by Birkhäuser-Verlag
- Subject
- Mathematics
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-003-0145-4
- Publisher site
- See Article on Publisher Site
Abstract
We give a new variational approach to L p -potential theory for sub-Markovian semigroups. It is based on the observation that the Gâteaux-derivative of the corresponding L p -energy functional is a monotone operator. This allows to apply the well established theory of Browder and Minty on monotone operators to the nonlinear problems in L p -potential theory. In particular, using this approach it is possible to avoid any symmetry assumptions of the underlying semigroup. We prove existence of corresponding ( r, p )-equilibrium potentials and obtain a complete characterization in terms of a variational inequality. Moreover we investigate associated potentials and encounter a natural interpretation of the so-called nonlinear potential operator in the context of monotone operators.
Journal
Journal of Evolution Equations – Springer Journals
Published: May 1, 2004