Papers by Giuseppe Devillanova
Analytical solutions for piles’ lateral deformations: The nonlinear stiffness case
International Journal of Mechanical Sciences
Integral symmetry conditions
Journal de Mathématiques Pures et Appliquées
CoFFEE: esperienze in contesti scolastici
École normale supérieure de Cachan - ENS Cachan, Oct 28, 2005
n co p Vq wr o s §t o r p r ¡uo p v ww x y x p z wo 8s #v ww x t q ww t { t x ¡uo z wo p V| 'w v ... more n co p Vq wr o s §t o r p r ¡uo p v ww x y x p z wo 8s #v ww x t q ww t { t x ¡uo z wo p V| 'w v ¡x t | )} wp cy )v Ṽr | ) ww o s §o F XX c| )} 'x uo x wuo &| ) ¡x o } ¡v wp Vq 9| )v wr { o r x y )t } wp Fz w| )s §y 't } wo p Fp ¡s uo x r t )v wo p ci )| )t r § ' o } q wy 'r x t { v ww t o r Fw o p #y 'v ¡x o v wr p #r )uo z wv wt p o } 'x w o §r ¡uo p v ww x y x z wo §s v ww x t q ww t { t x wuo g y { o w v wt Vz wo w o ¡t p x o } w{ o o } { | 'v wq wy )} 'x w o §z w| 's §y )t } wo o } !v w} } w| )s # wr o 9} wt Vz wo p | 'v wp z w| )s §y 't } wo p &z wo #s g o s §o F )r y '} wz wo v wr 8o x Sq wv wt p 8o } { | 'w w y )} 'x 8w o p 8p | 'w v ¡x t | )} wp Xx r | )v ¡i Vuo o p Sp v wr 8{ wy ) )v wo Fx r y )} w{ wo w o wt p x o } w{ o Fz wo #p | 'w v ¡x t | )} wp &o } } w| 's wr o Ft } ¡ 9} wt i wt o } )x Sz wo Fw y §q 9| )p p t wt w t x ¡uo Sz wo F{ w| )t p t r &y )r wt x r y 't r o s §o } )x w o F} w| 's wr o Sz wo Sx r y )} w{ wo p Xo x ¡q o z y 'q wq wr | ¡{ wo g} wo gq o v ¡x §q wy )p o x r o gy 'q wq ww t ¡v Vuo )v wy )} wz | )} x r y i 'y 't w w o §z wy )} wp v w} z w| )s §y 't } wo z wo | 'r s §o r ¡uo 'v ww t o r o c| )v wr w o p z w| )s §y 't } wo p §p ws uo x r t ¡v wo p gy 'v wp p t S{ o w y q o v ¡x ©uo { w| 'v wo r ¡v wy '} wz ©| )} r o { wo r { Xuo z wo p §r ¡uo p v ww x y x p §z wo s v ww x t q ww t { t x wuo z v w} x wq 9o q wy )r x t { v ww t o r Xq wy )r §o wo s §q ww o w o p §p | )w v ¡x t | '} wp r y )z wt y 'w o p V )v wy )} wz w o 8z w| )s §y 't } wo 8o p x 8v w} wo 8 | 'v ww o ' n co 8{ y 'p &r y 'z wt y )w wq o r s §o x &o } § y )t x Xz wo Sz w| '} w} wo r Xr )uo p v ww x y 'x p z o wt p x o } w{ o #o x Sz wo F} w| )} o wt p x o } w{ o #{ | 's §q ww uo s §o } )x y 't r o p &o } { | )r r o p q | '} wz wy )} w{ o #q wr ¡uo { t p o ' 8 ¡t c ¦ o x o p x 8v w} wo S | 'v ww o ' wy 'w | )r p Xq | 'v wr Xx | 'v ¡x S g © g XX Xy z wo p &p | 'w v ¡x t | )} wp Xr y )z wt y 'w o p Xo } g} w| )s # wr o St } ¡ 9} wt )v wt { wy )} w 'o } 'x #z wo #p t )} wo i )| )t r # Vy '} wz p t ¡ g¢ £¢ ¤ t w y v w} wo { | )} wp x y '} )x o § w¥ F z wo p | 'r x o ¡v wo XX #} y q wy )p z wo p | 'w v ¡x t | )} ! ¡v wt X{ wy )} w 'o gz wo p t '} wo p t 8 ©¦ w § & w¥ X i )| )t r 8 !8t } wp t Xw y { | '} wz wt x t | )} I C z wy '} wp 8w o Sr ¡uo p v ww x y x 8z o wt p x o } w{ o Fq wr ¡uo { 9uo z wo } )x S} wo Fq o v ¡x Sq wy 'p F o x r o uo w t s §t } Vuo o ' © Fy '} { o #{ wy 'q wt x r o #w y )v wo p x t | '} z wo #w o ¡t p x o } w{ o #z wo p | 'w v ¡x t | )} wp &o } } w| )s # wr o #t } ¡ 9} wt cy 'v Ṽr | ' ww o s §o XX q | 'v wr #{ wy ) )v wo gz w| 's §y )t } wo §r )uo )v ww t o r ª « ¬ S z wy '} wp w o §{ y 'p l g ) V| ' ¡x t o } 'x v w} wo r ¡uo q 9| )} wp o y '® §r s §y 'x t i )o n y } w| 'v ¡i )o w w o §t z Vuo o § )v wt V} w| )v wp Fy q o r s §t p Fz wo §q wr | 'v ¡i )o r #w o ¡t p x o } w{ o §z v w} wo §t } ¡ 9} wt x ¡uo z wo p | )w v ¡x t | '} wp Fy 'v Ṽr | ' ww o s §o g XX Fy ©uo x ¡uo §{ o w w o z wo §{ wy )} w 'o r Fw o §{ | )} w{ o q ¡x z wo ¯ ¡v wy 'p t Vp | )w v ¡x t | '} w°go x #z wo q wr | )v ¡i )o r 8w y §{ | 's §q wy ){ t x wuo Fq 9| )v wr 8{ o #} w| 'v ¡i )o w c| ' ¡± o x &² V} g y )t x 8w o F{ | )} w{ o q ¡x S wy ) wt x v wo w z wo # )v wy )p t cp | 'w v ¡x t | )} z Xuo q 9o } wz wy '} )x z wo w y } w| 'r s §o §³ !ẃµ #z wo §w y z Xuo r t i Vuo o z wo § ¶ 9r ¡uo { wo x §z wo §w uo } wo r 't o ' )v wt X{ | '} wz wv wt x y w y } w| ' x t | )} wt o } { | )} w} )v wo z wo p ¡uo )v wo } w{ o p FX 9 } wo q 9o r s §o x Fq wy )p Sz wo z Vuo z wv wt r o z wo p Fr )uo p v ww x y 'x p Sz wo { | )s §q wy '{ t x ¡uo z wy )} wp #{ o { | )} 'x o )x o ' !n co p p )uo ¡v wo } w{ o p §X | '} )x uo x ¡uo r o s §q ww y ){ 9uo o p q wy 'r z wo p p )uo ¡v wo } w{ o p §z wo p | )w v ¡x t | '} wp z wo §q wr | ' ww o s §o p Fy )q wq wr | ¡t s §y 'x t p y 'q wq o w uo o p ¯p ¡uo )v wo } w{ o p !uo )v wt w t wr ¡uo o p °! ¯ wy 'w y )} w{ o z !p o ¡v wo } w{ o p °o } y )} w 'w y )t p cn y F{ t r { | '} wp x y )} w{ o & )v wo &• wFo p x Vv w} wo &p | )w v ¡x t | '} #z v w} q wr | ) ww o s §o Xy )v ¡x | '} w| )s §o Xz wv s g o s §o Vx ¡q o ¡v wo §w o Ṽr | ' ww o s §o g XX S} w| )v wp Fq o r s §o x #z uo x y ' ww t r Sv w} wo §t } Xuo 'y )w t x ¡uo #w | ¡{ y 'w o z wo #x ¡q o §c| ) w| '¹ y 'o i ! )v wt { w y 't r o s §o } )x )x t o } )x &{ | 's §q ¡x o Sz wo Sw y #s §| ¡z wt 9{ y 'x t | '} §z wo Sw uo } wo r 't o « ģ r o w y 'x t i )o 8y 'v q wr | ) ww o s §o Sy 'q wq wr | wt s §y 'x t wº 9 p t s §o cr o w y 'x t i )o s §o } 'x Vy 'v ¡ { | )} w{ o } 'x r y 'x t | '} wp V» S} q wr | )v ¡i )o &o } q wr o s §t o r w t o v # ¡v wo &s g o s §o Xq 9| )v wr w o p cp v wt x o p #uo )v wt w t wr ¡uo o p cw t s §t x wuo o p c )v wo &w | )} #p v wq wq 9| )p o X} w| )} #{ | 's §q wy ){ x o p ct w ) #y Sw o Vs o s §o Vq w Xuo } w| 's o } wo Xz wo { | '} w{ o } )x r y x t | )} ¡v wt p o 8i Vuo r t 9o Fq 9| )v wr &w o p &p )uo ¡v wo } w{ o p SX } w| '} g{ | 's §q wy ){ x o p V² V} x r y i 'y 't w w y )} 'x &y i )o { Fw o p p ¡uo )v wo } w{ o p X} w| )} §{ | )s §q wy '{ x o p uo ¡v wt w t wr )uo o p o x Xo } §{ wy )} w 'o y '} )x Xw o v wr Vq wy 'r y )s uo x r o r z wo 8{ | )} w{ o } 'x r y 'x t | '} §| )} q o v ¡x 8q wr | ¡z wv wt r o Sv w} wo Ss §| ¡z wt 9{ y x t | )} §w | ¡{ y 'w o 8z wo Fw y F | )} w{ x t | )} w} wo w w o Sy 'q wq wr | wt s §y x t i )o S )v wt o p x 8z wv gs o s §o | )r z wr o z wo w y § | )} w{ x t | )} o } { | '} )x r y 'z wt { x t | '} y i )o { §w o F y )t x F )v wo §w o p uo w uo s §o } )x p Sz v w} wo p v wt x o uo )v wt w t wr ¡uo o p | )} 'x 8z wo p &q | 't } )x p X{ r t x t )v wo p Vn y #i 'y )r t y x t | )} §z wo Sw y # | '} w{ x t | '} w} wo w w o 8p | 'v wp &{ o x x o Fs §| ¡z wt 9{ y 'x t | '} §w | ¡{ y 'w o Sy uo x ¡uo guo i 'y )w v Vuo o Sq wy 'r Xv w} wo St } Xuo 'y )w t x ¡uo &w | ¡{ y 'w o 8z wo 8x wq 9o S| ' w| )¹ y )o i o x &v w} wo So p x t s §y 'x t | '} ¼ F½ 9¾ ¿ À ¾ ¿ 9v w} wt | 'r s §o
Elements of set theory and recursive arguments
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2021
These notes reflect partially the contents of a lecture given by the second author during the Int... more These notes reflect partially the contents of a lecture given by the second author during the International Workshop on New Horizons in Teaching Science in Messina on June 2018. The intention of this lecture was to present a concise and self–contained introduction to the construction of the real field as the unique, up to increasing isomorphism, Dedekind complete totally ordered field.
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2021
By using the preliminary results given in a previous divulgative note, we present here a concise ... more By using the preliminary results given in a previous divulgative note, we present here a concise and self–contained introduction to the construction of the real field as the unique, up to increasing isomorphism, Dedekind complete totally ordered field. Moreover, we also show the equivalence between the Dedekind completeness property on totally ordered fields and some meaningful well–known notions present in the literature, such as the Cauchy completeness on totally ordered Archimedean fields. This characterization result allows us to correctly encode the Dedekind completeness for totally ordered fields in the general abstract setting of metric spaces. We believe that the essential parts of the paper can be easily accessed by anyone with some experience in abstract mathematical thinking. The paper completes the lecture given by the second author during the International Workshop on New Horizons in Teaching Science in Messina on June 2018.
The role of planar symmetry and of symmetry constraints in the proof of existence of solutions to some scalar field equations
Nonlinear Analysis, 2020
Abstract This paper deals with some recent results for scalar field equations in the case of a po... more Abstract This paper deals with some recent results for scalar field equations in the case of a potential which converges from above to a limit at infinity. In particular, we shall collect some of the results of the authors which have contributed to partially answer a conjecture of Wei and Yan and we shall announce some results in a forthcoming paper to the aim of giving a short survey which collects the main ideas based on the use of symmetry assumptions and of symmetry methods introduced for the above problem.
The paper studies existence of solutions for the nonlinear Schrdinger equation (0.1) − (∇+ iA(x))... more The paper studies existence of solutions for the nonlinear Schrdinger equation (0.1) − (∇+ iA(x))u+ V (x)u = f(|u|)u with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is required. Solutions are obtained by means of a general structural statement about bounded sequences in the magnetic Sobolev space.
Advances in Differential Equations, 2002
In this paper, we consider the problem −Δu = |u| 2 * −2 u+λu in Ω, u = 0 on ∂Ω, where Ω is an ope... more In this paper, we consider the problem −Δu = |u| 2 * −2 u+λu in Ω, u = 0 on ∂Ω, where Ω is an open regular bounded subset of R N (N ≥ 3), 2 * = 2N N −2 is the critical Sobolev exponent and λ > 0. Our main result asserts that, if N ≥ 7, the problem has infinitely many solutions and, from the point of view of the compactness arguments employed here, the restriction on the dimension N cannot be weakened.
arXiv: Functional Analysis, 2018
For many known non-compact embeddings of two Banach spaces $E\hookrightarrow F$, every bounded se... more For many known non-compact embeddings of two Banach spaces $E\hookrightarrow F$, every bounded sequence in $E$ has a subsequence that takes form of a profile decomposition - a sum of clearly structured terms with asymptotically disjoint supports plus a remainder that vanishes in the norm of $F$. In this note we construct a profile decomposition for arbitrary sequences in the Sobolev space $H^{1,2}(M)$ of a compact Riemannian manifold, relative to the embedding of $H^{1,2}(M)$ into $L^{2^*}(M)$, generalizing the well-known profile decomposition of Struwe ([Proposition 2.1]{Struwe}) to the case of arbitrary bounded sequences.
Profile Decomposition in Metric Spaces
Surface instabilities in graded tubular tissues induced by volumetric growth
International Journal of Non-Linear Mechanics, 2020
Abstract Growth-induced pattern formation in tubular tissues is intimately correlated to normal p... more Abstract Growth-induced pattern formation in tubular tissues is intimately correlated to normal physiological functions. Moreover, either the microstructure or certain diseases can give rise to material inhomogeneity, which can lead to a change of shape in the tissue. Therefore, it is of fundamental importance to understand surface instabilities and pattern transitions of graded tubular tissues. In this paper we perform such analysis by the use of a mechanical model of a graded tube which grows with a fixed outer boundary by focusing on a plane-strain problem within the framework of nonlinear elasticity. A theoretical model is established to determine the uniform growth state, the critical growth factor, and the critical wavenumber for a general material model and for a general material gradient. For a case study, the material is specified by the neo-Hookean model, and the shear modulus is assumed to decay linearly or exponentially from the inner surface. Then, a parametric study is carried out to unravel the effects of material and geometrical parameters on the bifurcation threshold and the associated wrinkled pattern. In addition, a finite element model, which is validated by the theoretical one, is developed to trace the post-buckling evolution. It is found that wrinkled pattern will evolve into an arch mode and then into a creasing mode if the modulus decays linearly. However, the typical creasing mode may give way to a period-doubling mode when applying an exponentially decaying modulus, and there is a co-existence of the creasing mode and the wrinkling mode. As a result, different modulus gradients can generate diverse pattern formations. The obtained results are useful to supply insight into the effects of material inhomogeneity and different modulus gradients on surface instabilities and morphology evolutions in graded tubular tissues.
Milan Journal of Mathematics, 2021
The paper studies the initial boundary value problem related to the dynamic evolution of an elast... more The paper studies the initial boundary value problem related to the dynamic evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction is aimed to model the phenomenon of attachment-detachment of the beam occurring in adhesion phenomena. We prove existence of solutions in energy space and exhibit various counterexamples to uniqueness. Furthermore we characterize some relevant features of the solutions, ruling the main effects of the nonlinearity due to the elastic-breakable term on the dynamical evolution, by proving the linearization property according to Gérard (J Funct Anal 141(1):60–98, 1996) and an asymptotic result pertaining the long time behavior.
Calculus of Variations and Partial Differential Equations, 2014
We show the existence of infinitely many positive solutions u ∈ H 1 (R 2) to the equation − u + a... more We show the existence of infinitely many positive solutions u ∈ H 1 (R 2) to the equation − u + a(x)u = u p , with p > 1 , without asking, on the positive potential a(x), any symmetry assumption as in Wei and Yan (
We discuss some basic properties of polar convergence in metric spaces. Polar convergence is clos... more We discuss some basic properties of polar convergence in metric spaces. Polar convergence is closely connected with the notion of Delta-convergence of T.C. Lim known for several years. Possible existence of a topology which induces polar convergence is also investigated. Some applications of polar convergence follow.
Elementary properties of optimal irrigation patterns
Calculus of Variations and Partial Differential Equations, 2006
ABSTRACT In this paper we follow the approach in Maddalena etal. (Interfaces and Free Boundaries ... more ABSTRACT In this paper we follow the approach in Maddalena etal. (Interfaces and Free Boundaries 5, 391–415, 2003) to the study of the ramified structures and we identify some geometrical properties enjoyed by optimal irrigation patterns. These properties are “elementary” in the sense that they are not concerned with the regularity at the ending points of such structures, where the presumable selfsimilarity properties should take place. This preliminary study already finds an application in G. Devillanova and S. Solimini (Math. J. Univ. Padua, to appear), where it is used in order to discuss the irrigability of a given measure.
In this note we prove formula (1.1),which extends to functions inW 2,2(�) with zero normal deriva... more In this note we prove formula (1.1),which extends to functions inW 2,2(�) with zero normal derivative the analogous formula (1.2) by G. Ta-lenti ([5]) on functions with zero trace. To prove (1.1) we use the techniqueintroduced by C. Miranda in [3] and give a geometrical interpretation of hisresults (formula (2.17)). 1. Introduction. Let � ⊆ Rn be a C2-smooth, bounded domain. Let u ∈W 2,2 (�) be suchthat u0 = ∂u ∂n = n�
Measure valued solutions for an optimal harvesting problem
Journal de Mathématiques Pures et Appliquées
The Journal of Geometric Analysis
In the present paper, we show how to define suitable subgroups of the orthogonal group $${O}(d-m)... more In the present paper, we show how to define suitable subgroups of the orthogonal group $${O}(d-m)$$ O ( d - m ) related to the unbounded part of a strip-like domain $$\omega \times {\mathbb {R}}^{d-m}$$ ω × R d - m with $$d\ge m+2$$ d ≥ m + 2 , in order to get “mutually disjoint” nontrivial subspaces of partially symmetric functions of $$H^1_0(\omega \times {\mathbb {R}}^{d-m})$$ H 0 1 ( ω × R d - m ) which are compactly embedded in the associated Lebesgue spaces. As an application of the introduced geometrical structure, we prove (existence and) multiplicity results for semilinear elliptic problems set in a strip-like domain, in the presence of a nonlinearity which either satisfies the classical Ambrosetti–Rabinowitz condition or has a sublinear growth at infinity. The main theorems of this paper may be seen as an extension of existence and multiplicity results, already appeared in the literature, for nonlinear problems set in the entire space $${\mathbb {R}}^d$$ R d , as for insta...
Nonlinear Schrödinger equation with bounded magnetic field
Journal of Differential Equations
Uploads
Papers by Giuseppe Devillanova