For variational integrals F(u) = ∫ Ωf(x,Du) dx defined on vector valued mappings u : Ω ⊂ R n → R N, we establish some structure conditions on f that enable us to prove local boundedness for minimizers u ∈ W 1,1(Ω;R N) of F. These structure conditions are satisfied in three remarkable examples: {equation presented}, for suitable convex functions {equation presented}.
Local boundedness for vector valued minimizers of anisotropic functionals / F. Leonetti; E. Mascolo. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - STAMPA. - Volume 31, Issue 3:(2012), pp. 357-378. [10.4171/ZAA/1464]
Local boundedness for vector valued minimizers of anisotropic functionals
MASCOLO, ELVIRA
2012
Abstract
For variational integrals F(u) = ∫ Ωf(x,Du) dx defined on vector valued mappings u : Ω ⊂ R n → R N, we establish some structure conditions on f that enable us to prove local boundedness for minimizers u ∈ W 1,1(Ω;R N) of F. These structure conditions are satisfied in three remarkable examples: {equation presented}, for suitable convex functions {equation presented}.
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