一类退化椭圆型方程边值问题的适定性

Well-Posedness of Boundary Value Problems for a Class of Degenerate Elliptic Equations

研究一类特殊退化椭圆型方程边值问题的适定性,该类问题与双曲空间中的极小图的Dirichlet问题,曲面的无穷小等距形变刚性问题等等的研究密切相关,而这类方程的特征形式在区域上是变号的,其适定性是值得深入讨论的.最后,得到这类边值问题的H^1弱解的存在性和唯一性.

This paper studies the well-posedness of boundary value problems for a special class of degenerate elliptic equations coming from geometry. Such problem is intimately tied to the Dirichlet probleln for minimal graphs in hyperbolic space, the rigidity problem arising in infinitesimal isolnetric de, formation of surface, etc. 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, the existence and uniqueness of H^1 weak solution for such problems is obtained.