Full regularity for convex integral functionals with p(x) growth in low dimensions

Habermann J (2010)

Publication Type: Journal article

Publication year: 2010

Journal

Bolletino dell Unione Matematica Italiana Unione Matematica Italiana

Publisher: Unione Matematica Italiana

Book Volume: IX, Vol. III

Pages Range: 521-541

Journal Issue: 3

Abstract

For ω ⊂ Rⁿ,n ≥ 2, and N ≥ 1 we consider vector valued minimizers u ε W^m,p(.) Ioc of a uniformly convex integral functional of the type F[u,ω] :=∫(x,D^mu) dx, a where f is a Carathéorody function satisfying p(x) growth conditions with respect to the second variable. We show that if the dimension n is small enough, dependent on the structure conditions of the functional, there holds D^ku ε C^0,B loc (ω)for k ε {0,...,m - 1}, for some ß, also depending on the structural data, provided that the nonlinearity exponent p is uniformly continuous with modulus of continuity ω satisfying lim supω(p)log(1/p) =0.

Authors with CRIS profile

Jens Habermann Naturwissenschaftliche Fakultät

How to cite

APA:

Habermann, J. (2010). Full regularity for convex integral functionals with p(x) growth in low dimensions. Bolletino dell Unione Matematica Italiana, IX, Vol. III(3), 521-541.

MLA:

Habermann, Jens. "Full regularity for convex integral functionals with p(x) growth in low dimensions." Bolletino dell Unione Matematica Italiana IX, Vol. III.3 (2010): 521-541.

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