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 [Formula presented]. To our knowledge, this is the first boundary regularity result under a non-standard p,q-growth condition.
CITATION STYLE
Bögelein, V., Duzaar, F., Marcellini, P., & Scheven, C. (2022). Boundary regularity for elliptic systems with p,q-growth. Journal Des Mathematiques Pures et Appliquees, 159, 250–293. https://doi.org/10.1016/j.matpur.2021.12.004
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