Higher integrability of the gradient for vectorial minimizers of decomposable variational integrals
نویسندگان
چکیده
منابع مشابه
Higher integrability of the gradient for vectorial minimizers of decomposable variational integrals
We consider local minimizers u: Rn ⊃ Ω → RN of variational integrals I[u] := ∫ Ω F (∇u) dx, where F is of anisotropic (p, q)-growth with exponents 1 < p ≤ q < ∞. If F is in a certain sense decomposable, we show that the dimensionless restriction q ≤ 2p+2 together with the local boundedness of u implies local integrability of ∇u for all exponents t ≤ p+2. More precisely, the initial exponents fo...
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We consider local minimizers u: R2 ⊃ Ω → RN of variational integrals like ∫ Ω[(1+ |∂1u|)+(1+ |∂2u|)] dx or its degenerate variant ∫ Ω[|∂1u|+ |∂2u|] dx with exponents 2 ≤ p < q < ∞ which do not fall in the category studied in [BF2]. We prove interior C1,αrespectively C1-regularity of u under the condition that q < 2p. For decomposable variational integrals of arbitrary order a similar result is ...
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2007
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-007-0096-0