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

Michela Eleuteri

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Regularity results for a class of quasiconvex functionals with nonstandard growth

Emilio Acerbi, Giuseppe Mingione (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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 $\int_{Ω} f (D u) d x,$ dove $f$ soddisfa l'ipotesi di crescita ${|ξ|}^{p} - c_{1} \leq f (ξ) \leq c (1 + {|ξ|}^{q}),$ con $1 < p < q \leq 2$ . 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 $\int f (x, D u) d x$ under non standard growth assumptions of $(p, q)$ -type: namely, we assume that ${|z|}^{p (x)} \leq f (x, z) \leq L (1 + {|z|}^{p (x)})$ , a relevant model case being the functional $\int {|D u|}^{p (x)} d x$ . 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.

$L^{2, λ}$ -regularity for minima of variational integrals

Josef Daněček, Eugen Viszus (2003)

Bollettino dell'Unione Matematica Italiana

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The $L^{2, λ}$ -regularity of the gradient of local minima for nonlinear functionals is shown.

Displaying similar documents to “Hölder continuity results for a class of functionals with non-standard growth”

Regularity results for a class of quasiconvex functionals with nonstandard growth

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Functionals with p ⁢ x growth and regularity

L 2 , λ -regularity for minima of variational integrals

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

Functionals with $p (x)$ growth and regularity

$L^{2, λ}$ -regularity for minima of variational integrals