Displaying similar documents to “Some estimates of solutions to Monge-Ampère type equations in dimension two”

An inverse problem for the equation ▵ u = - c u - d

Michael Vogelius (1994)

Annales de l'institut Fourier

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Let Ω be a bounded, convex planar domain whose boundary has a not too degenerate curvature. In this paper we provide partial answers to an identification question associated with the boundary value problem ▵ u = - c u - d in Ω , u = 0 on ∂ Ω . We prove two results: 1) If Ω is not a ball and if one considers only solutions with - c u - d ≤ 0 , then there exist at most finitely many pairs of coefficients ( c , d ) so that the normal derivative ∂ u ∂ ν | ∂ Ω equals a given ψ ≠ 0 . 2) If one imposes no sign condition on the...