Functionals with $p(x)$ growth and regularity

Emilio Acerbi; Giuseppe Mingione

Displaying similar documents to “Functionals with $p (x)$ growth and regularity”

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 $\int f (x, u, D u)$ under non-standard growth conditions of $p (x)$ -type, i.e. $L^{- 1} {|z|}^{p (x)} \leq f (x, s, z) \leq L (1 + {|z|}^{p (x)})$ 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 $\int_{Ω} f (D u) d x,$ 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.

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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Partial regularity of minimizers of quasiconvex integrals with subquadratic growth: the general case

Menita Carozza, Giuseppe Mingione (2001)

Annales Polonici Mathematici

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We prove partial regularity for minimizers of the functional $\int_{Ω} f (x, u (x), D u (x)) d x$ where the integrand f(x,u,ξ) is quasiconvex with subquadratic growth: $| f (x, u, ξ) | \leq L (1 + | ξ |^{p})$ , p < 2. We also obtain the same results for ω-minimizers.

Morrey regularity and continuity results for almost minimizers of asymptotically convex integrals

Mikil Foss, Antonia Passarelli di Napoli, Anna Verde (2008)

Applicationes Mathematicae

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In a recent paper [Forum Math., 2008] the authors established some global, up to the boundary of a domain Ω ⊂ ℝⁿ, continuity and Morrey regularity results for almost minimizers of functionals of the form $u \mapsto \int_{Ω} g (x, u (x), \nabla u (x)) d x$ . The main assumptions for these results are that g is asymptotically convex and that it satisfies some growth conditions. In this article, we present a specialized but significant version of this general result. The primary purpose of this paper is provide several applications of this...

On the interior regularity of weak solutions of degenerate elliptic systems (the case $1$ < $p$ < $2$ )

J. Naumann, J. Wolf (1992)

Rendiconti del Seminario Matematico della Università di Padova

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Displaying similar documents to “Functionals with p ⁢ x growth and regularity”

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

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

Regularity results for a class of quasiconvex functionals with nonstandard growth

Partial regularity of minimizers of quasiconvex integrals with subquadratic growth: the general case

Morrey regularity and continuity results for almost minimizers of asymptotically convex integrals

On the interior regularity of weak solutions of degenerate elliptic systems (the case 1 &lt; p &lt; 2 )

Displaying similar documents to “Functionals with $p (x)$ growth and regularity”

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

On the interior regularity of weak solutions of degenerate elliptic systems (the case $1$ < $p$ < $2$ )