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Let be a CM-finite Artin algebra with a Gorenstein-Auslander generator , be a Gorenstein projective -module and . We give an upper bound for the finitistic dimension of in terms of homological data of . Furthermore, if is -Gorenstein for , then we show the global dimension of is less than or equal to plus the -projective dimension of As an application, the global dimension of is less than or equal to .
This paper deals with local boundedness for minimizers of vectorial integrals under anisotropic growth conditions by using De Giorgi’s iterative method. We consider integral functionals with the first part of the integrand satisfying anisotropic growth conditions including a convex nondecreasing function , and with the second part, a convex lower order term or a polyconvex lower order term. Local boundedness of minimizers is derived.
We are interested in regularizing effect of the interplay between the coefficient of zero order term and the datum in some noncoercive integral functionals of the type
where , is a Carathéodory function such that is convex, and there exist constants and such that
for almost all , all and all . We show that, even if and only belong to , the interplay
implies the existence of a minimizer which belongs to .
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