Elvira Mascolo - Academia.edu (original) (raw)
Papers by Elvira Mascolo
Advances in Calculus of Variations, 2008
We prove a lower semicontinuity theorem for a polyconvex functional of integral form, related to ... more We prove a lower semicontinuity theorem for a polyconvex functional of integral form, related to maps u W R n ! R m in W 1;n . I R m / with n m 2, with respect to the weak W 1;p -convergence for p > m 1, without assuming any coercivity condition.
La Matematica Nella Societa E Nella Cultura Rivista Della Unione Matematica Italiana Serie I, 2012
Annali Dell Universita Di Ferrara, 1979
Nonlinear Analysis: Theory, Methods & Applications, 2016
Ricerche Di Matematica, 1979
Rendiconti Lincei - Matematica e Applicazioni, 2016
Annales Academiae Scientiarum Fennicae Mathematica, 2015
Contemporary Mathematics, 2013
ABSTRACT The authors present a method to get local boundedness for the minimizers u:Ω⊂ℝ n →ℝ m , ... more ABSTRACT The authors present a method to get local boundedness for the minimizers u:Ω⊂ℝ n →ℝ m , n≥2, m≥1, u∈W 1,1 (Ω;ℝ m ), of the integral ∫ Ω f(x,Du)dx without assuming any condition on the boundary data. The integrand is supposed to have anisotropic behaviour with respect to the m×n matrix ξ=(ξ i α ) ∑ i=1 n |ξ i | p i ≤f(x,ξ)≤c1+∑ i=1 n |ξ i | q with suitable exponents 1≤p i ≤q· The machinery relies on reduction to the corresponding Euler system and application of the Moser iteration technique.
Some results on sharp multiplicity of solutions for semilinear elliptic boundary value problems a... more Some results on sharp multiplicity of solutions for semilinear elliptic boundary value problems are given in this paper. First, the problem Δu+f(u)=h in G, u=ϕ on ∂G, under suitable assumptions on f, and where G is an open bounded domain in ℝ N , is studied, and results in the very well-known paper by A. Ambrosetti and G. Prodi [Ann. Mat. Pura Appl., IV. Ser. 93, 231- 246 (1972; Zbl 0288.35020)] are extended to the case ϕ≠0. In section 2, results asserting the existence of exactly three solutions due to A. Ambrosetti and G. Mancini [Nonlinear Anal., Theory Methods Appl. 3, 635-645 (1979; Zbl 0433.35025)] for h=0 and ϕ=0 are extended to small h and ϕ. Finally, it is shown that the problem u '' +f(u)=0, where f is C 2 and f ' (t)<1, has as many 2π- periodic solutions as zeroes has f.
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Les auteurs montrent l’existence d’au moins une solution lipschitzienne pour un problème de calcu... more Les auteurs montrent l’existence d’au moins une solution lipschitzienne pour un problème de calcul des variations du type Min{∫ G f(Dv(x))dx|v=u 0 sur ∂G} où G est un ouvert borné de ℝ n , f est une fonction réelle continue non nécessairement convexe sur ℝ n et vérifie les conditions suivantes: a) L’ensemble K={p∈ℝ n |f(p)>f ** (p)} est borné, f ** étant la bipolaire de f. b) f ** est affine sur K, et u 0 est une fonction réelle lipschitzienne qui satisfait à une condition ”de pente bornée”.
Die Arbeit beschäftigt sich mit schwachen Lösungen des Problems (1)-∑ i,j (a ij u x j ) x i +c(x)... more Die Arbeit beschäftigt sich mit schwachen Lösungen des Problems (1)-∑ i,j (a ij u x j ) x i +c(x)u=λuinG;u=0auf∂G·G⊂ℝ m ist eine offene beschränkte Menge; die Koeffizienten a ij sind meßbare und beschränkte Funktionen mit ∑ i,j a ij ξ i ξ j ≥|ξ| 2 ; c(x) ist nichtnegativ und meßbar. Die Verff. beweisen Abschätzungen für ess sup u, wobei u die positive, L 2 -normierte Eigenfunktion zum 1. Eigenwert des Problems (1) ist. Eine der Abschätzungen gilt nur für m=3, die andere für 2≤m<6. Das Maximum von u kann jeweils allein durch den Eigenwert und das Maß von G abgeschätzt werden. Der Beweis arbeitet mit einer Symmetrisierungs-Technik (rearrangement of functions) und stützt sich wesentlich auf ein Ergebnis von G. Talenti [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 3, 697-718 (1976; Zbl 0341.35031)].
ABSTRACT Riassunto In questo lavoro ci occupiamo di problemi al contorno per una classe di operat... more ABSTRACT Riassunto In questo lavoro ci occupiamo di problemi al contorno per una classe di operatori lineari quasi ellittici del tipoA+σ, dove σ è una perturbazione assegnata; proviamo che l'operatore associato al problema è di Fredholm con indice zero e studiamo le proprietà spettrali dell'operatore associato al problema con condizioni al contorno omogenee.
]ELVII~A MASCOLO SUMMARY A compactness theorem for weighted Sobolcv spaces in R ~ is proved, with... more ]ELVII~A MASCOLO SUMMARY A compactness theorem for weighted Sobolcv spaces in R ~ is proved, without requiring that the weight function to be infinite at infinity. The theorem generalizes some recent results of V. ]3E~'cI and D. Fo~'rUNATO .
Advances in Calculus of Variations, 2008
We prove a lower semicontinuity theorem for a polyconvex functional of integral form, related to ... more We prove a lower semicontinuity theorem for a polyconvex functional of integral form, related to maps u W R n ! R m in W 1;n . I R m / with n m 2, with respect to the weak W 1;p -convergence for p > m 1, without assuming any coercivity condition.
La Matematica Nella Societa E Nella Cultura Rivista Della Unione Matematica Italiana Serie I, 2012
Annali Dell Universita Di Ferrara, 1979
Nonlinear Analysis: Theory, Methods & Applications, 2016
Ricerche Di Matematica, 1979
Rendiconti Lincei - Matematica e Applicazioni, 2016
Annales Academiae Scientiarum Fennicae Mathematica, 2015
Contemporary Mathematics, 2013
ABSTRACT The authors present a method to get local boundedness for the minimizers u:Ω⊂ℝ n →ℝ m , ... more ABSTRACT The authors present a method to get local boundedness for the minimizers u:Ω⊂ℝ n →ℝ m , n≥2, m≥1, u∈W 1,1 (Ω;ℝ m ), of the integral ∫ Ω f(x,Du)dx without assuming any condition on the boundary data. The integrand is supposed to have anisotropic behaviour with respect to the m×n matrix ξ=(ξ i α ) ∑ i=1 n |ξ i | p i ≤f(x,ξ)≤c1+∑ i=1 n |ξ i | q with suitable exponents 1≤p i ≤q· The machinery relies on reduction to the corresponding Euler system and application of the Moser iteration technique.
Some results on sharp multiplicity of solutions for semilinear elliptic boundary value problems a... more Some results on sharp multiplicity of solutions for semilinear elliptic boundary value problems are given in this paper. First, the problem Δu+f(u)=h in G, u=ϕ on ∂G, under suitable assumptions on f, and where G is an open bounded domain in ℝ N , is studied, and results in the very well-known paper by A. Ambrosetti and G. Prodi [Ann. Mat. Pura Appl., IV. Ser. 93, 231- 246 (1972; Zbl 0288.35020)] are extended to the case ϕ≠0. In section 2, results asserting the existence of exactly three solutions due to A. Ambrosetti and G. Mancini [Nonlinear Anal., Theory Methods Appl. 3, 635-645 (1979; Zbl 0433.35025)] for h=0 and ϕ=0 are extended to small h and ϕ. Finally, it is shown that the problem u '' +f(u)=0, where f is C 2 and f ' (t)<1, has as many 2π- periodic solutions as zeroes has f.
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Les auteurs montrent l’existence d’au moins une solution lipschitzienne pour un problème de calcu... more Les auteurs montrent l’existence d’au moins une solution lipschitzienne pour un problème de calcul des variations du type Min{∫ G f(Dv(x))dx|v=u 0 sur ∂G} où G est un ouvert borné de ℝ n , f est une fonction réelle continue non nécessairement convexe sur ℝ n et vérifie les conditions suivantes: a) L’ensemble K={p∈ℝ n |f(p)>f ** (p)} est borné, f ** étant la bipolaire de f. b) f ** est affine sur K, et u 0 est une fonction réelle lipschitzienne qui satisfait à une condition ”de pente bornée”.
Die Arbeit beschäftigt sich mit schwachen Lösungen des Problems (1)-∑ i,j (a ij u x j ) x i +c(x)... more Die Arbeit beschäftigt sich mit schwachen Lösungen des Problems (1)-∑ i,j (a ij u x j ) x i +c(x)u=λuinG;u=0auf∂G·G⊂ℝ m ist eine offene beschränkte Menge; die Koeffizienten a ij sind meßbare und beschränkte Funktionen mit ∑ i,j a ij ξ i ξ j ≥|ξ| 2 ; c(x) ist nichtnegativ und meßbar. Die Verff. beweisen Abschätzungen für ess sup u, wobei u die positive, L 2 -normierte Eigenfunktion zum 1. Eigenwert des Problems (1) ist. Eine der Abschätzungen gilt nur für m=3, die andere für 2≤m<6. Das Maximum von u kann jeweils allein durch den Eigenwert und das Maß von G abgeschätzt werden. Der Beweis arbeitet mit einer Symmetrisierungs-Technik (rearrangement of functions) und stützt sich wesentlich auf ein Ergebnis von G. Talenti [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 3, 697-718 (1976; Zbl 0341.35031)].
ABSTRACT Riassunto In questo lavoro ci occupiamo di problemi al contorno per una classe di operat... more ABSTRACT Riassunto In questo lavoro ci occupiamo di problemi al contorno per una classe di operatori lineari quasi ellittici del tipoA+σ, dove σ è una perturbazione assegnata; proviamo che l'operatore associato al problema è di Fredholm con indice zero e studiamo le proprietà spettrali dell'operatore associato al problema con condizioni al contorno omogenee.
]ELVII~A MASCOLO SUMMARY A compactness theorem for weighted Sobolcv spaces in R ~ is proved, with... more ]ELVII~A MASCOLO SUMMARY A compactness theorem for weighted Sobolcv spaces in R ~ is proved, without requiring that the weight function to be infinite at infinity. The theorem generalizes some recent results of V. ]3E~'cI and D. Fo~'rUNATO .