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Displaying similar documents to “Existence and boundedness of minimizers of a class of integral functionals”

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.

Partial Hölder continuity results for solutions of non linear non variational elliptic systems with limit controlled growth

Luisa Fattorusso, Giovanna Idone (2002)

Bollettino dell'Unione Matematica Italiana

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Let Ω be a bounded open subset of R n , n > 4 , of class C 2 . Let u H 2 Ω a solution of elliptic non linear non variational system a x , u , D u , H u = b x , u , D u where a x , u , μ , ξ and b x , u , μ are vectors in R N , N 1 , measurable in x , continuous in u , μ , ξ and u , μ respectively. Here, we demonstrate that if b x , u , μ has limit controlled growth, if a x , u , μ , ξ is of class C 1 in ξ and satisfies the Campanato condition A and, together with a ξ , certain continuity assumptions, then the vector D u is partially Hölder continuous for every exponent α < 1 - n p .

One-dimensional symmetry for solutions of quasilinear equations in R 2

Alberto Farina (2003)

Bollettino dell'Unione Matematica Italiana

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In this paper we consider two-dimensional quasilinear equations of the form div a u u + f u = 0 and study the properties of the solutions u with bounded and non-vanishing gradient. Under a weak assumption involving the growth of the argument of u (notice that arg u is a well-defined real function since u > 0 on R 2 ) we prove that u is one-dimensional, i.e., u = u ν x for some unit vector ν . As a consequence of our result we obtain that any solution u having one positive derivative is one-dimensional. This result provides...

Homogenization of some nonlinear problems with specific dependence upon coordinates

P. Courilleau, S. Fabre, J. Mossino (2001)

Bollettino dell'Unione Matematica Italiana

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Questo articolo considera una successione di equazioni differenziali a derivate parziali non lineari in forma di divergenza del tipo - div Q ϵ G x , N ϵ u = f ϵ , in un dominio limitato Ω dello spazio n -dimensionale; Q ϵ = Q ϵ x e N ϵ = N ϵ x sono matrici con coefficenti limitati, N ϵ e è invertibile e la sua matrice inversa R ϵ ha anche coefficenti limitati. La non linearità è dovuta alla funzione G = G x , ξ ; la condizione di crescita, la monotonicità e le ipotesi di coercitività sono modellate sul p -Laplaciano, 1 < p < , ed assicurano l'esistenza di...

Γ -convergence of constrained Dirichlet functionals

Gian Paolo Leonardi (2003)

Bollettino dell'Unione Matematica Italiana

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Given an open, bounded and connected set Ω R n with Lipschitz boundary and volume Ω , we prove that the sequence F k of Dirichlet functionals defined on H 1 Ω ; R d , with volume constraints v k on m 2 fixed level-sets, and such that i = 1 m v i k < Ω for all k , Γ -converges, as v k v with i = 1 m v i k = Ω , to the squared total variation on B V V ; R d , with v as volume constraint on the same level-sets.