Partial regularity of minimizers of higher order integrals with (p,q)-growth
ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 2, p. 472-492

We consider higher order functionals of the form F[u]= Ω f(D m u)dxforu: n Ω N , where the integrand f: m ( n , N ) , m 1 is strictly quasiconvex and satisfies a non-standard growth condition. More precisely we assume that f fulfills the (p, q)-growth condition γ|A| p f(A)L(1+|A| q )forallA m ( n , N ), with γ, L > 0 and 1<pq<minp + 1 n , 2n-1 2n-2 p. We study minimizers of the functional F[·] and prove a partial C loc m,α -regularity result.

DOI : https://doi.org/10.1051/cocv/2010016
Classification:  49N60,  49N99,  49J45
Keywords: higher order functionals, non-standard growth, regularity theory
@article{COCV_2011__17_2_472_0,
     author = {Schemm, Sabine},
     title = {Partial regularity of minimizers of higher order integrals with $(p, q)$-growth},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {2},
     year = {2011},
     pages = {472-492},
     doi = {10.1051/cocv/2010016},
     zbl = {1248.49053},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2011__17_2_472_0}
}
Schemm, Sabine. Partial regularity of minimizers of higher order integrals with $(p, q)$-growth. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 2, pp. 472-492. doi : 10.1051/cocv/2010016. http://www.numdam.org/item/COCV_2011__17_2_472_0/

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