A second order problem with nonlocal boundary conditions

Authors: Todorov Todor D.

Keywords: well-posedness; unconstrained minimization problem; nonlocal boundary conditions

DOI: 10.5937/SPSUNP1802071T

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Abstract:

A second order elliptic problem with nonlocal boundary conditions is the object of interest in this paper. The strong problem is reduced into a unconstrained minimization one. Sufficient conditions for existence and uniqueness of the weak solution are proved. A priory estimates for the weak solution are obtained.