Regularity of $\omega$-minimizers of quasi-convex variational integrals with polynomial growth

Duzaar F, Kronz M (2002)

Publication Type: Journal article

Publication year: 2002

Journal

Differential Geometry and its Applications Elsevier

Publisher: Elsevier

Book Volume: 17

Pages Range: 139-152

Journal Issue: 2-3

URI: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TYY-46B4N65-4-B3&_cdi=5631&_user=616145&_orig=search&_coverDate=09%2F30%2F2002&_sk=999829997&view=c&wchp=dGLbVtz-zSkzV&md5=04f186a6d48102cbdc0bdf90fa2a463e&ie=/sdarticle.pdf

DOI: 10.1016/S0926-2245(02)00104-3

Abstract

We consider almost respectively strong almost minimizers to quasi-convex variational integrals. Under a polynomial growth condition on the integrand and conditions on the function ω determing the almost minimality, in particular the assumption that Ω (r) = ∫0^r √ω(ρ)ρ^-1 dρ is finite for some r > 0, we establish almost everywhere C¹-regularity for almost minimizers. Under the weaker assumption that ω is bounded and lim ρ↓0 ω(ρ)=0 we prove almost everywhere C^0,α-regularity for strong almost minimizers to quasi-convex variational integrals of quadratic growth.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations Manfred Kronz Department Mathematik

How to cite

APA:

Duzaar, F., & Kronz, M. (2002). Regularity of $\omega$-minimizers of quasi-convex variational integrals with polynomial growth. Differential Geometry and its Applications, 17(2-3), 139-152. https://dx.doi.org/10.1016/S0926-2245(02)00104-3

MLA:

Duzaar, Frank, and Manfred Kronz. "Regularity of $\omega$-minimizers of quasi-convex variational integrals with polynomial growth." Differential Geometry and its Applications 17.2-3 (2002): 139-152.

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