TY - JOUR

T1 - Variational integrals on Orlicz-Sobolev spaces

AU - Fuchs, M.

AU - Osmolovski, V.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - We consider vector functions u : ℝn ⊃ Ω → ℝN minimizing variational integrals of the form ∫Ω G(∇u) dx with convex density G whose growth properties are described in terms of an N-function A : [0,∞) →[0,∞) with lim supt→∞ A(t)t-2 < ∞. We then prove - under certain technical assumptions on G - full regularity of u provided that n = 2, and partial C1-regularity in the case n ≥ 3. The main feature of the paper is that we do not require any power growth of G.

AB - We consider vector functions u : ℝn ⊃ Ω → ℝN minimizing variational integrals of the form ∫Ω G(∇u) dx with convex density G whose growth properties are described in terms of an N-function A : [0,∞) →[0,∞) with lim supt→∞ A(t)t-2 < ∞. We then prove - under certain technical assumptions on G - full regularity of u provided that n = 2, and partial C1-regularity in the case n ≥ 3. The main feature of the paper is that we do not require any power growth of G.

KW - Minima

KW - Orlicz-Sobolev spaces

KW - Regularity theory

KW - Variational problems

UR - http://www.scopus.com/inward/record.url?scp=22044431678&partnerID=8YFLogxK

U2 - 10.4171/ZAA/829

DO - 10.4171/ZAA/829

M3 - Article

AN - SCOPUS:22044431678

VL - 17

SP - 393

EP - 415

JO - Zeitschrift für Analysis und ihre Anwendungen

JF - Zeitschrift für Analysis und ihre Anwendungen

SN - 0232-2064

IS - 2

ER -