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On the hyperbolic Dirichlet to Neumann functional. (English) Zbl 0940.35124
Summary: We prove the injectivity of the linearization of the hyperbolic Dirichlet to Neumann functional associated to metrics near the Euclidean one in a “small” bounded domain of $$\mathbb{R}^3$$, under some suitable transversality and geometric conditions.
##### MSC:
 35L20 Initial-boundary value problems for second-order hyperbolic equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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