We consider the integral functional with nearly-linear growth int;Ω |Du| log(1+|Du|)dx where u : Ω ⊂ ℝn → ℝN (n ≥ 2, N ≥ 1) and we prove that any local minimizer u has locally Hölder continuous gradient in the interior of Ω thus excluding the presence of singular sets in Ω. This functional has recently been considered by several authors in connection with variational models for problems from the theory of plasticity with logarithmic hardening. We also give extensions of this result to more general cases. © Heldermann Verlag.

Full C1, α-regularity for minimizers of integral functionals with L log L-growth / Mingione, G.; Siepe, F.. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - 18:4(1999), pp. 1083-1100. [10.4171/ZAA/929]

Full C1, α-regularity for minimizers of integral functionals with L log L-growth

Mingione G.
;
1999-01-01

Abstract

We consider the integral functional with nearly-linear growth int;Ω |Du| log(1+|Du|)dx where u : Ω ⊂ ℝn → ℝN (n ≥ 2, N ≥ 1) and we prove that any local minimizer u has locally Hölder continuous gradient in the interior of Ω thus excluding the presence of singular sets in Ω. This functional has recently been considered by several authors in connection with variational models for problems from the theory of plasticity with logarithmic hardening. We also give extensions of this result to more general cases. © Heldermann Verlag.
1999
Full C1, α-regularity for minimizers of integral functionals with L log L-growth / Mingione, G.; Siepe, F.. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - 18:4(1999), pp. 1083-1100. [10.4171/ZAA/929]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2895062
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