Displaying similar documents to “Regularity results for a class of quasiconvex functionals with nonstandard growth”

Hölder continuity results for a class of functionals with non-standard growth

Michela Eleuteri (2004)

Bollettino dell'Unione Matematica Italiana

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We prove regularity results for real valued minimizers of the integral functional ∫ f ⁢ x , u , D ⁢ u under non-standard growth conditions of p ⁢ x -type, i.e. L - 1 ⁢ z p ⁢ x ≤ f ⁢ x , s , z ≤ L ⁢ 1 + z p ⁢ x under sharp assumptions on the continuous function p ⁢ x > 1 .

Functionals with p ⁢ x growth and regularity

Emilio Acerbi, Giuseppe Mingione (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We consider the integral functional ∫ f ⁢ x , D ⁢ u ⁢ d ⁢ x under non standard growth assumptions of p , q -type: namely, we assume that z p ⁢ x ≤ f ⁢ x , z ≤ L ⁢ 1 + z p ⁢ x , a relevant model case being the functional ∫ D ⁢ u p ⁢ x ⁢ d ⁢ x . Under sharp assumptions on the continuous function p ⁢ x > 1 we prove regularity of minimizers both in the scalar and in the vectorial case, in which we allow for quasiconvex energy densities. Energies exhibiting this growth appear in several models from mathematical physics.