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In this paper we give some new results on second order differentialoperator equations of elliptic type with nonregular boundary conditions with coefficient-operator. The study is developped in H¨ spaces and uses the reduction method of S. G. Krein. Necessary and sufficient conditions of compatibility are established to obtain different types of solutions. Maximal regularity properties are also studied.

On some elliptic problems with nonlocal boundary coefficient-operator conditions in the framework of Hölderian spaces