Non-local approximation of functionals: variational and evolution problems

Massimo Gobbino

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Displaying similar documents to “Non-local approximation of functionals: variational and evolution problems”

Discrete approximation of the Mumford-Shah functional in dimension two

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The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of vergence by a sequence of integral functionals defined on piecewise affine functions.

Hölder continuity results for a class of functionals with non-standard growth

Michela Eleuteri (2004)

Bollettino dell'Unione Matematica Italiana

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We prove regularity results for real valued minimizers of the integral functional $\int f (x, u, D u)$ under non-standard growth conditions of $p (x)$ -type, i.e. $L^{- 1} {|z|}^{p (x)} \leq f (x, s, z) \leq L (1 + {|z|}^{p (x)})$ under sharp assumptions on the continuous function $p (x) > 1$ .