We study the regularity of weak solutions to the elliptic system in divergence form divA( x , D u)=0 in an open set Ω of R n , n ≥2. The vector field A( x .ξ), A: Ω×R m×n →R m×n , has a variational nature in the sense that A( x ,ξ)= D ξ f ( x ,ξ), where f :Ω×R m×n →R is a convex Caratheodory integrand ; i.e., f = f ( x ,ξ) is measurable with respect to x ∈R n and it is a convex function with respect to ξ∈R m×n . If m =1 then the system reduces to a partial differential equation . In the context m >1 of general vector-valued maps and systems , a classical assumption finalized to the everywhere regularity of the weak solutions is a modulus-dependence in the energy integrand; i.e., we require that f ( x ,ξ)= g ( x ,|ξ|), where g :Ω×[0,∞)→[0,∞) is measurable with respect to x∈ R n and it is a convex and increasing function with respect to the gradient variable t∈[0,∞).
{"title":"Regularity for nonlinear elliptic equations and systems","authors":"Paolo Marcellini","doi":"10.1478/AAPP.98S2A10","DOIUrl":"https://doi.org/10.1478/AAPP.98S2A10","url":null,"abstract":"We study the regularity of weak solutions to the elliptic system in divergence form divA( x , D u)=0 in an open set Ω of R n , n ≥2. The vector field A( x .ξ), A: Ω×R m×n →R m×n , has a variational nature in the sense that A( x ,ξ)= D ξ f ( x ,ξ), where f :Ω×R m×n →R is a convex Caratheodory integrand ; i.e., f = f ( x ,ξ) is measurable with respect to x ∈R n and it is a convex function with respect to ξ∈R m×n . If m =1 then the system reduces to a partial differential equation . In the context m >1 of general vector-valued maps and systems , a classical assumption finalized to the everywhere regularity of the weak solutions is a modulus-dependence in the energy integrand; i.e., we require that f ( x ,ξ)= g ( x ,|ξ|), where g :Ω×[0,∞)→[0,∞) is measurable with respect to x∈ R n and it is a convex and increasing function with respect to the gradient variable t∈[0,∞).","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48161709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Speech held on 19 September 2019 during the Opening Ceremony of the Workshop on Variational Analysis, PDEs, and Mathematical Economics, on the occasion of Antonino Maugeri's 75th birthday.
{"title":"L'Università italiana nella seconda metà del Novecento e l'inizio della carriera accademica del prof. Antonino Maugeri","authors":"M. Marino","doi":"10.1478/AAPP.98S2E3","DOIUrl":"https://doi.org/10.1478/AAPP.98S2E3","url":null,"abstract":"Speech held on 19 September 2019 during the Opening Ceremony of the Workshop on Variational Analysis, PDEs, and Mathematical Economics, on the occasion of Antonino Maugeri's 75th birthday.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49603798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper contains some results of existence of infinitely many solutions to an elliptic equation involving the p(x) - biharmonic operator coupled with Navier boundary conditions where the nonlinearities depend on two real parameters and do not possess any symmetric property. The approach is variational and the main tool is an abstract result of Ricceri.
{"title":"Sequences of weak solutions to a fourth-order elliptic problem","authors":"F. Cammaroto","doi":"10.1478/AAPP.98S2A3","DOIUrl":"https://doi.org/10.1478/AAPP.98S2A3","url":null,"abstract":"This paper contains some results of existence of infinitely many solutions to an elliptic equation involving the p(x) - biharmonic operator coupled with Navier boundary conditions where the nonlinearities depend on two real parameters and do not possess any symmetric property. The approach is variational and the main tool is an abstract result of Ricceri.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43329693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present an existence theorem for a class of generalized quasi-variational problem involving Grassmannian manifolds. This class is directly inspired by a general equilibrium problem with time, uncertainty and incomplete financial market with real assets. The problem of the existence of this equilibrium cannot be analyzed using standard techniques employed in similar models. Then, we show how the concept of equilibrium is strictly related to the concept of Grassmannian manifolds. Finally, we present a variational inequality problem, whose solutions are equilibria of the proposed model.
{"title":"An existence theorem for generalized quasi-variational inequalities involving the Grassmannian manifold with an application","authors":"M. B. Donato, Antonio Villanacci","doi":"10.1478/AAPP.98S2A6","DOIUrl":"https://doi.org/10.1478/AAPP.98S2A6","url":null,"abstract":"We present an existence theorem for a class of generalized quasi-variational problem involving Grassmannian manifolds. This class is directly inspired by a general equilibrium problem with time, uncertainty and incomplete financial market with real assets. The problem of the existence of this equilibrium cannot be analyzed using standard techniques employed in similar models. Then, we show how the concept of equilibrium is strictly related to the concept of Grassmannian manifolds. Finally, we present a variational inequality problem, whose solutions are equilibria of the proposed model.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43615020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Luigi d’Onofrio, C. Sbordone, Roberta Schiattarella
Let E be a Banach space with a supremum type norm induced by a collection of functionals ℒ ⊂ X * where X is a reflexive Banach space. Familiar spaces of this type are BMO , BV , C 0,α (0 1. For most of these spaces E , the predual E * exists and can be defined by atomic decomposition of its elements. Another typical result, when it is possible to define a rich vanishing subspace E 0 ⊂ E is the "two star theorem", namely ( E 0 )*= E * . This fails for E = BV and E = C 0,1 = Lip .
{"title":"Duality and o − O-structure in non reflexive Banach spaces","authors":"Luigi d’Onofrio, C. Sbordone, Roberta Schiattarella","doi":"10.1478/AAPP.98S2A7","DOIUrl":"https://doi.org/10.1478/AAPP.98S2A7","url":null,"abstract":"Let E be a Banach space with a supremum type norm induced by a collection of functionals ℒ ⊂ X * where X is a reflexive Banach space. Familiar spaces of this type are BMO , BV , C 0,α (0 1. For most of these spaces E , the predual E * exists and can be defined by atomic decomposition of its elements. Another typical result, when it is possible to define a rich vanishing subspace E 0 ⊂ E is the \"two star theorem\", namely ( E 0 )*= E * . This fails for E = BV and E = C 0,1 = Lip .","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43249306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose an interpretation of heat in a multi-scale continuum representation of sparse media dynamics. We attribute the emergence of heat processes to residual fluctuations beyond average and meso-scale affine dynamics.
{"title":"Preamble to the analysis of thermodynamic processes in sparse phases","authors":"G. Capriz, P. M. Mariano","doi":"10.1478/AAPP.982A5","DOIUrl":"https://doi.org/10.1478/AAPP.982A5","url":null,"abstract":"We propose an interpretation of heat in a multi-scale continuum representation of sparse media dynamics. We attribute the emergence of heat processes to residual fluctuations beyond average and meso-scale affine dynamics.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49383260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By using γ-operations on an m -structure and a hereditary class H, we define the notion of γ-compactness modulo hereditary classes (or ideals) called γH-compact. We obtain several properties of γH-compact spaces and γH-compact sets relative to m -structures.
{"title":"Properties of γH-compact spaces with hereditary classes","authors":"A. Al-Omari, T. Noiri","doi":"10.1478/AAPP.982A4","DOIUrl":"https://doi.org/10.1478/AAPP.982A4","url":null,"abstract":"By using γ-operations on an m -structure and a hereditary class H, we define the notion of γ-compactness modulo hereditary classes (or ideals) called γH-compact. We obtain several properties of γH-compact spaces and γH-compact sets relative to m -structures.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46166341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Literature mechanical relaxation data of amorphous selenium are interpreted in terms of the soft potential model and its extension to higher temperatures, the Gilroy-Phillips model. At the crossover temperature from tunneling states to thermally activated relaxation, one finds a stronger decrease of the barrier density f(V) with increasing barrier height V than in silica. On the high barrier side, f(V) is determined by the Kohlrausch t β -tail of the viscous flow, with β = 0.31. In longitudinal ultrasound absorption data, one finds weak oscillations of the Kohlrausch barrier density, similar to those found recently in metallic glasses, consistent with an increase of the barrier by V 1 = S 1 T g /β for the addition of one selenium atom to the rearranging domain, where S 1 is the structural entropy per atom at the glass temperature T g .
文献中非晶硒的机械弛豫数据是根据软势模型及其对更高温度的扩展，即Gilroy-Phillips模型来解释的。在从隧穿态到热激活弛豫的交叉温度下，发现势垒密度f（V）随着势垒高度V的增加而比在二氧化硅中更强地降低。在高阻侧，f（V）由粘性流的Kohlrausch tβ-尾确定，其中β=0.31。在纵向超声吸收数据中，我们发现Kohlrausch势垒密度的微弱振荡，类似于最近在金属玻璃中发现的振荡，与在重排结构域中添加一个硒原子时势垒增加V1=S1 T g/β一致，其中S1是玻璃温度T g下每个原子的结构熵。
{"title":"Mechanical relaxation in amorphous selenium","authors":"U. Buchenau, G. D’Angelo, G. Carini, Xiao Liu","doi":"10.1478/AAPP.98S1A4","DOIUrl":"https://doi.org/10.1478/AAPP.98S1A4","url":null,"abstract":"Literature mechanical relaxation data of amorphous selenium are interpreted in terms of the soft potential model and its extension to higher temperatures, the Gilroy-Phillips model. At the crossover temperature from tunneling states to thermally activated relaxation, one finds a stronger decrease of the barrier density f(V) with increasing barrier height V than in silica. On the high barrier side, f(V) is determined by the Kohlrausch t β -tail of the viscous flow, with β = 0.31. In longitudinal ultrasound absorption data, one finds weak oscillations of the Kohlrausch barrier density, similar to those found recently in metallic glasses, consistent with an increase of the barrier by V 1 = S 1 T g /β for the addition of one selenium atom to the rearranging domain, where S 1 is the structural entropy per atom at the glass temperature T g .","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44887883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
V. Nibali, C. Branca, A. Paciaroni, U. Wanderlingh, G. D’Angelo
We review the main achievements accomplished in the study of the coherent collective dynamics of phospholipid membranes, i.e. , the collective vibrational excitations active on the sub-picoseconds to picoseconds time scale and terahertz frequencies, over a length scale comparable to the angstrom length scale. The first descriptions of the terahertz collective spectrum, mainly assigned to a single longitudinal acoustic-like mode similarly to simple liquids, have been progressively replaced by a complex scenario, with longitudinal and transverse acoustic-like and optic-like inelastic excitations. Complex phenomena (avoided crossing mechanisms between modes, a phonon gap introduced by the disorder and a slow- to fast-sound transition) have been highlighted in the dispersion curves of lipid bilayers. Systematic and comprehensive studies along the lines of the investigations reviewed here contribute to understand the role of the collective (coherent) chain dynamics in the passive transport across bilayers, in the formation of water wires inside dynamic defects in lipid bilayers and in other biological functions of biomembranes.
{"title":"Coherent collective dynamics in phospholipid membranes: where are we now?","authors":"V. Nibali, C. Branca, A. Paciaroni, U. Wanderlingh, G. D’Angelo","doi":"10.1478/AAPP.98S1A10","DOIUrl":"https://doi.org/10.1478/AAPP.98S1A10","url":null,"abstract":"We review the main achievements accomplished in the study of the coherent collective dynamics of phospholipid membranes, i.e. , the collective vibrational excitations active on the sub-picoseconds to picoseconds time scale and terahertz frequencies, over a length scale comparable to the angstrom length scale. The first descriptions of the terahertz collective spectrum, mainly assigned to a single longitudinal acoustic-like mode similarly to simple liquids, have been progressively replaced by a complex scenario, with longitudinal and transverse acoustic-like and optic-like inelastic excitations. Complex phenomena (avoided crossing mechanisms between modes, a phonon gap introduced by the disorder and a slow- to fast-sound transition) have been highlighted in the dispersion curves of lipid bilayers. Systematic and comprehensive studies along the lines of the investigations reviewed here contribute to understand the role of the collective (coherent) chain dynamics in the passive transport across bilayers, in the formation of water wires inside dynamic defects in lipid bilayers and in other biological functions of biomembranes.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47484902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The disordered topology introduces additional degrees of freedom in the structure of amorphous solids mainly enhancing the local atomic mobility. This gives rise to substantial and amazing changes of the physical properties of these systems compared to the corresponding crystals, i.e. solids having the same stoichiometry, but over an ordered structure. In this article, the possible connection between the thermodynamic and vibrational aspects of glasses and the topological disorder is considered, emphasizing the most significant differences between crystalline and amorphous solids having the same stoichiometry.
{"title":"Effects of topological disorder on thermodynamic and vibrational properties of amorphous solids","authors":"G. D’Angelo, G. Carini","doi":"10.1478/AAPP.98S1A1","DOIUrl":"https://doi.org/10.1478/AAPP.98S1A1","url":null,"abstract":"The disordered topology introduces additional degrees of freedom in the structure of amorphous solids mainly enhancing the local atomic mobility. This gives rise to substantial and amazing changes of the physical properties of these systems compared to the corresponding crystals, i.e. solids having the same stoichiometry, but over an ordered structure. In this article, the possible connection between the thermodynamic and vibrational aspects of glasses and the topological disorder is considered, emphasizing the most significant differences between crystalline and amorphous solids having the same stoichiometry.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49263905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：