ENERGY-FINITE SOLUTIONS OF Au = Pu AND DIRICHLET MAPPINGS

@inproceedings{Glasner2010ENERGYFINITESO,
  title={ENERGY-FINITE SOLUTIONS OF Au = Pu AND DIRICHLET MAPPINGS},
  author={Moses Glasner},
  year={2010}
}
Let R, S be noncompact Riemannian m-manifolds and let T:R—>S be a Dirichlet mapping. Consider a nonnegative locally bounded measurable m-iorm P on R and set Q—T*lP, the pull-back of P under r-1. Denote by PE(R) {QE(S) resp.) the space of energy-finite solutions of Au=Pu on R (Au = Qu on 5 resp.). The spaces PE(R) and QE(S) are isomorphic, the isomorphism being bicontinuous with respect to the energy norms and preserves the sup norm of bounded solutions. Let R, S be noncompact Riemannian w… 

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