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Regularity of minimizers of vectorial integrals with p−q growth

✍ Scribed by Giovanni Cupini; Marcello Guidorzi; Elvira Mascolo

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
260 KB
Volume
54
Category
Article
ISSN
0362-546X

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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) = r 0 √ ω(ρ)ρ -1 dρ is finite for some r > 0,

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We prove higher integrability for minimizers u : 0 Ä R N of integral functionals 0 ( f (Du)+a(x) u) dx, where f satisfies a non standard growth condition of ( p, q) type, |z| p f (z) L(1+|z| q ), p<q.