We prove the existence of second weak derivatives for bounded minimizers u: Ω ⊂ Rn → RN of the integral ∫Ω(|Du|2 + |Dnu|q) dx, when 2 < q ≤ 2(n − 1)/(n − 3), n ≥ 4. This allows us to improve on the Hausdorff dimension of the singular set of u.
Differentiability for bounded minimizers of some anisotropic integrals / Canale, A.; D'Ottavio, A.; Leonetti, F.; Longobardi, Maria. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 253:2(2001), pp. 640-650. [doi.org/10.1006/jmaa.2000.7186]
Differentiability for bounded minimizers of some anisotropic integrals
LONGOBARDI, MARIA
2001
Abstract
We prove the existence of second weak derivatives for bounded minimizers u: Ω ⊂ Rn → RN of the integral ∫Ω(|Du|2 + |Dnu|q) dx, when 2 < q ≤ 2(n − 1)/(n − 3), n ≥ 4. This allows us to improve on the Hausdorff dimension of the singular set of u.File in questo prodotto:
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