Abstract
We study some non linear and non elliptic boundary value problems obtained by considering a non linear elliptic second order partial differential equation and a non linear first order boundary condition. Relying on well-known linear results and using the Nash-Moser-type technique of a generalized implicit function theorem of Zehnder, we construct local solutions which are not smooth up to the boundary. Consequently well-known results about the non elliptic linear oblique derivative problem are extended to the non linear case.
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