Energy-finite solutions of $\Delta u=Pu$ and Dirichlet mappings
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- by Moses Glasner PDF
- Proc. Amer. Math. Soc. 29 (1971), 553-556 Request permission
Abstract:
Let R, S be noncompact Riemannian m-manifolds and let $T:R \to S$ be a Dirichlet mapping. Consider a nonnegative locally bounded measurable m-form P on R and set $Q = T_\ast ^{ - 1}P$, the pull-back of P under ${T^{ - 1}}$. Denote by $PE(R)\;(QE(S)$ resp.) the space of energy-finite solutions of $\Delta u = Pu$ on R ($\Delta u = Qu$ on S 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.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 553-556
- MSC: Primary 53.72; Secondary 30.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279734-X
- MathSciNet review: 0279734