Direct variational methods in nonreflexive spaces
Jozef Kačur, Jiří Souček · Czech digital mathematics library · 1979
In the present paper we investigate the variational problems of the type of a nonparametric minimal surface by means of direct methods.Let us consider the nonparametric minimal surface problem.We are looking for the minimum of the functional J(и,ß) = í (l + |Vи| 2 ) 1/2 dд: Ja on the set of functions with a prescribed boundary condition u = q? on 3Q.It is natural to look in the case of this problem for a weak solution in the Sobolev space W\(Q) and to take the boundary condition W\, which has a compact ball in some weak topology.The following conditions must be satisfied if we want to use the direct methods for a larger space W^ZD W\: