Displaying similar documents to “Global existence and regularity of solutions for complex Ginzburg-Landau equations”

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...

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 .

Existence and boundedness of minimizers of a class of integral functionals

A. Mercaldo (2003)

Bollettino dell'Unione Matematica Italiana

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In this paper we consider a class of integral functionals whose integrand satisfies growth conditions of the type f ( x , η , ξ ) a ( x ) | ξ | p ( 1 + | η | ) α - b 1 ( x ) | η | β 1 - g 1 ( x ) , f ( x , η , 0 ) b 2 ( x ) | η | β 2 + g 2 ( x ) , where 0 α < p , 1 β 1 < p , 0 β 2 < p , α + β i p , a x , b i x , g i x ( i = 1 , 2 ) are nonnegative functions satisfying suitable summability assumptions. We prove the existence and boundedness of minimizers of such a functional in the class of functions belonging to the weighted Sobolev space W 1 , p a , which assume a boundary datum u 0 W 1 , p a L Ω .

Composition operators on Banach spaces of formal power series

B. Yousefi, S. Jahedi (2003)

Bollettino dell'Unione Matematica Italiana

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Let β n n = 0 be a sequence of positive numbers and 1 p < . We consider the space H p β of all power series f z = n = 0 f n z n such that n = 0 f n p β n p < . Suppose that 1 p + 1 q = 1 and n = 1 n q j β n q = for some nonnegative integer j . We show that if C φ is compact on H p β , then the non-tangential limit of φ j + 1 has modulus greater than one at each boundary point of the open unit disc. Also we show that if C φ is Fredholm on H p β , then φ must be an automorphism of the open unit disc.