| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 841086 | Nonlinear Analysis: Theory, Methods & Applications | 2012 | 7 Pages |
Abstract
We consider the boundary value problem {∑i=1nDi(ai(x,Du(x)))=0,x∈Ω;u(x)=u∗(x),x∈∂Ω. We show that, higher integrability of the boundary datum u∗u∗ forces solutions uu to have higher integrability as well. Assumptions on ai(x,z)ai(x,z) are suggested by the Euler equation of the anisotropic functional ∫Ω(|D1u|p1+|D2u|p2+⋯+|Dnu|pn)dx.∫Ω(|D1u|p1+|D2u|p2+⋯+|Dnu|pn)dx.
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Authors
Francesco Leonetti, Francesco Siepe,