The strong Legendre condition and the well-posedness of mixed Robin problems on manifolds with bounded geometry
by
Bernd Ammann, Nadine Große, Victor Nistor


The strong Legendre condition and the well-posedness of mixed Robin problems on manifolds with bounded geometry (.pdf)

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Short Abstract

Let M be a smooth manifold with (smooth) boundary ∂M and bounded geometry and ∂DM ⊂ ∂M be an open and closed subset. We prove the well-posedness of the mixed Robin boundary value problem Pu = f in M, u = 0 on ∂DM, ∂Pν u + bu = 0 on ∂M \ ∂DM under the following assumptions. First, we assume that P satisfies the strong Legendre condition (which reduces to the uniformly strong ellipticity condition in the scalar case) and that it has totally bounded coefficients (that is, that the coefficients of P and all their derivatives are bounded). Let ∂RM ⊂ ∂M \ ∂DM be the set where b≠ 0.

An extended abstract is in the file.


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The Paper was written on 8.8.2018
Last update 11.9.2018