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We are concerned with the following PDE: ,
in
,
, on
, where
is a bounded domain of
, and
is a given function. We provide a complete description of the loss of compactness of the equation under the assumption that K is strictly decreasing in the outward normal direction on
and flat near its critical points. As product, we prove an existence result through an Euler–Poincaré characteristic argument.
No potential conflict of interest was reported by the author.
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