Well-posedness of boundary value problems for a class of second order degenerate elliptic equations

In this paper, we study the well-posedness of boundary value problems for a special class of degenerate elliptic equations coming from geometry. Such problems is intimately tied to rigidity problem arising in infinitesimal isometric deformation, The characteristic form of this class of equations is changing its signs in the domain. Therefore the well-posedness of these above problems deserve to make a further discussion. Finally, we get the existence and uniqueness of $H^1$ solution for such boundary value problems.