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- W4200508051 abstract "We investigate the boundary regularity of minimizers of convex integral functionals with nonstandard p,q-growth and with Uhlenbeck structure. We consider arbitrary convex domains Ω and homogeneous Dirichlet data on some part Γ⊂∂Ω of the boundary. For the integrand we assume only a non-standard p,q-growth condition. We establish Lipschitz regularity of minimizers up to Γ, provided the gap between the growth exponents p and q is not too large, more precisely if 1<p≤q<p(1+2n). To our knowledge, this is the first boundary regularity result under a non-standard p,q-growth condition. Nous étudions la régularité jusque'à la frontière des minimiseurs de fonctions intégrales convexes avec une croissance p,q non standard et avec une structure Uhlenbeck. Nous considérons des domaines convexes arbitraires Ω et des données de Dirichlet homogènes sur une partie Γ⊂∂Ω de la frontière. Pour l'intégrande, nous supposons seulement une condition de croissance p,q non standard. Nous établissons la régularité Lipschitz des minimiseurs jusqu'à Γ, à condition que l'écart entre les exposants de croissance p et q ne soit pas trop grand, plus précisément si 1<p≤q<p(1+2n). A notre connaissance, il s'agit du premier résultat de régularité jusque'à la frontière sous une condition de croissance p,q non standard." @default.
- W4200508051 created "2021-12-31" @default.
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- W4200508051 date "2022-03-01" @default.
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- W4200508051 title "Boundary regularity for elliptic systems with p,q-growth" @default.
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- W4200508051 doi "https://doi.org/10.1016/j.matpur.2021.12.004" @default.
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