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.

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DOI Code:
10.1285/i15900932v19n2p231
Classification:
49J45
Full Text: PDF