DOI: 10.68381/jca18009 ISSN: 0944-6532

Higher Integrability for Solutions to Variational Problems with Fast Growth

Arrigo Cellina, Marco Mazzola
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We prove higher integrability properties of solutions to variational problems of minimizing

\int_\Omega [e^{f(\|\nabla u(x)\|)}+g(x,u(x))]\,dx ∫ Ω [ e f ( ∥ ∇ u ( x ) ∥ ) + g ( x , u ( x ) ) ]   d x
where
f f
is a convex function satisfying some additional conditions

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