On the Relaxation of Some Types of Dirichlet Minimum Problems for Unbounded Functionals

Abstract

In this paper, considered a Borel function g on taking its values in , verifying some weak hypothesis of continuity, such that and is convex, we obtain an integral representation result for the lower semicontinuous envelope in the - topology of the integral functional , where(Error rendering LaTeX formula) only on suitable pin is of the boundary of that lie, for example, on affine spaces orthogonal to , for boundary values satisfying suitable compatibility conditions and is geometrically well situated respect to . Then we apply this result to Dirichlet nunimum problems.