Displaying similar documents to “A result on equiabsolute integrability”

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 .

Gradient regularity for minimizers of functionals under p - q subquadratic growth

F. Leonetti, E. Mascolo, F. Siepe (2001)

Bollettino dell'Unione Matematica Italiana

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Si prova la maggior sommabilità del gradiente dei minimi locali di funzionali integrali della forma ∫ Ω f ⁢ D ⁢ u ⁢ d ⁢ x , dove f soddisfa l'ipotesi di crescita ξ p - c 1 ≤ f ⁢ ξ ≤ c ⁢ 1 + ξ q , con 1 < p < q ≤ 2 . L'integrando f è C 2 e D ⁢ D ⁢ f ha crescita p - 2 dal basso e q - 2 dall'alto.

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.

Local boundedness for minimizers of variational integrals under anisotropic nonstandard growth conditions

Zesheng Feng, Aiping Zhang, Hongya Gao (2024)

Czechoslovak Mathematical Journal

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This paper deals with local boundedness for minimizers of vectorial integrals under anisotropic growth conditions by using De Giorgi’s iterative method. We consider integral functionals with the first part of the integrand satisfying anisotropic growth conditions including a convex nondecreasing function g , and with the second part, a convex lower order term or a polyconvex lower order term. Local boundedness of minimizers is derived.