- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 20:06:52
11
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RLM&vol=28&iss=2&update_since=2024-03-28
Rendiconti Lincei - Matematica e Applicazioni
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.
RLM
1120-6330
1720-0768
General
10.4171/RLM
http://www.ems-ph.org/doi/10.4171/RLM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
28
2017
2
Uniqueness and stability in triple porosity thermoelasticity
Brian
Straughan
University of Durham, DURHAM, UNITED KINGDOM
Thermoelasticity, triple porosity, stability, uniqueness
A general model for a triple porosity thermoelastic solid is presented in the linear anisotropic case. This allows for cross coupling of inertia coefficients, and cross coupling of interaction coefficients representing actions between pressures in the macro, meso and micro structures. Sufficient conditions are derived to demonstrate uniqueness and stability when the elastic coefficients are, in a precise sense, positive. Uniqueness is further demonstrated in the dynamical problem when the elastic coefficients are not sign-definite and possess only the major symmetry. An indication is given as to how one would proceed to obtain continuous dependence upon the inital data in the Hölder sense. The proof of uniqueness in the indefinite elasticity tensor case involves a logarithmic convexity method which proceeds by a novel choice of functional.
Mechanics of deformable solids
191
208
10.4171/RLM/758
http://www.ems-ph.org/doi/10.4171/RLM/758
On the equations governing nonlinear symmetric Kirchhoff’s elastic rods
Edvige
Pucci
Università degli Studi di Perugia, PERUGIA, ITALY
Giuseppe
Saccomandi
Università degli Studi di Perugia, PERUGIA, ITALY
Rods mechanics, Lancret’s helices, Kirchhoff’s Kinetic Analogy
A systematic study of the equations governing the nonlinear symmetric Kirchhoff elastic rods is proposed. Symmetric rods are characterized by the conservation of the contact torque along the tangent of the centre line of the rod. This additional conservation law enables the formal reduction to quadratures of the governing equations and a systematic study of general (or Lancret’s) helical solutions. This improves previous analyses where only solutions relative to the case when the centre line is a circular helix have been investigated. Moroever, we consider the general helical solution for inhomogeneous symmetric rods and, conclusively, we study a special solution where the contact torque along the tangent of the centre line is zero. This solution is valid also for asymmetric Kirchhoff rods.
Mechanics of deformable solids
209
227
10.4171/RLM/759
http://www.ems-ph.org/doi/10.4171/RLM/759
Upper and lower estimates of multicomponent convection instability threshold via auxiliary Bénard problems
Salvatore
Rionero
Università degli Studi di Napoli Federico II, NAPOLI, ITALY
Multi-component mixtures, convection, instability threshold, upper and lower estimates, global stability, Bénard auxiliary systems
The onset of convection in a $m$-component Navier–Stokes fluid mixture, filling a horizontal layer $\texttt L$ heated from below and salted partly from above and partly from below, $\forall m \in \mathbb N$, is investigated. The difficulties of handling this nonlinear problem, grow drastically with $m$ and only under special circumstances the instability threshold can be given in algebraic simple closed form. Then the problem of finding, in simple algebraic closed forms, suitable lower and upper estimates of the instability threshold arises. In the present paper, for any type of boundary (rigid-rigid, one rigid-one free, free-free), it is shown that: 1) a linearization principle in the energy norm holds; 2) upper and lower estimates of the instability threshold can be obtained via auxiliary classical Bénard problems. The estimates obtained appear to be of interest not only for theoreticians but also for experimentalists investigating natural phenomena and/or industrial processes related to the onset of convection.
Fluid mechanics
Partial differential equations
229
253
10.4171/RLM/760
http://www.ems-ph.org/doi/10.4171/RLM/760
New frontiers in Zanaboni’s formulation of Saint-Venant’s principle
Robin
Knops
Heriot-Watt University, EDINBURGH, UNITED KINGDOM
Saint-Venant’s principle, piezoelectricity, thermolasticity
A synoptic account is presented of a revised Zanaboni procedure for Saint-Venant’s principle. Modifications required for conservative and dissipative coupled systems are illustrated by application to piezoelectricity and thermoelasticity.
Partial differential equations
Mechanics of deformable solids
255
275
10.4171/RLM/761
http://www.ems-ph.org/doi/10.4171/RLM/761
Integral points on the complement of the branch locus of projections from hypersurfaces
Andrea
Ciappi
Scuola Normale Superiore, PISA, ITALY
Integral points, diophantine equations, diophantine geometry
We study the integral points on $\mathbb P_n \setminus D$, where $D$ is the branch locus of a projection from a hypersurface in $\mathbb P_{n+1}$ to a hyperplane $H \simeq \mathbb P_n$. We extend to the general case a result by Zannier (whose approach we follow) and we also obtain a sharper bound that yields, in some cases, the finiteness of integral points. The results presented are effective and the proofs provide a way to actually construct a set containing all the integral points in question. Thus, there are concrete applications to the study of Diophantine equations, more precisely to the problem of finding integral solutions to equations $F(x_0, \dots, x_n) = c$, where $c$ is a given nonzero value and $F$ is a homogeneous form defining the branch locus $D$, i.e. a discriminant.
Number theory
277
291
10.4171/RLM/762
http://www.ems-ph.org/doi/10.4171/RLM/762
Analytical mechanics and Levi-Civita’s parallel transport
Giuseppe
Iurato
Università di Palermo, PALERMO, ITALY
Riemannian manifold, Levi-Civita’s parallel transport, virtual work principle, linear connection
This historical note is a detailed, technical reconstruction of the crucial role played by Lagrange’s principle of virtual work in working out the fundamental notion of parallel transport on a Riemannian manifold described in the original Levi-Civita’s argument.
History and biography
Differential geometry
Mechanics of particles and systems
293
304
10.4171/RLM/763
http://www.ems-ph.org/doi/10.4171/RLM/763
Comparison results for nonlinear anisotropic parabolic problems
Angela
Alberico
Consiglio Nazionale delle Ricerche, NAPOLI, ITALY
Giuseppina
di Blasio
Università degli Studi della Campania “Luigi Vanvitelli”, CASERTA, ITALY
Filomena
Feo
Università degli Studi di Napoli 'Parthenope', NAPOLI, ITALY
Anisotropic symmetrization, anisotropic parabolic problems, a priori estimate
Comparison results for solutions to the Dirichlet problems for a class of nonlinear, anisotropic parabolic equations are established. These results are obtained through a semi-discretization method in time after providing estimates for solutions to anisotropic elliptic problems with zero-order terms.
Partial differential equations
305
322
10.4171/RLM/764
http://www.ems-ph.org/doi/10.4171/RLM/764
Networks self-similarly moving by curvature with two triple junctions
Pietro
Baldi
Università degli Studi di Napoli Federico II, NAPOLI, ITALY
Emanuele
Haus
Università di Napoli Federico II, NAPOLI, ITALY
Carlo
Mantegazza
Università di Napoli Federico II, NAPOLI, ITALY
Network, evolution, curvature, self-shrinking
We prove that there are no networks homeomorphic to the Greek ‘‘Theta’’ letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees, such that under the motion by curvature they are self-similarly shrinking. This fact completes the classification of the self-similarly shrinking networks in the plane with at most two triple junctions, see [5, 7, 18].
Differential geometry
323
338
10.4171/RLM/765
http://www.ems-ph.org/doi/10.4171/RLM/765
On some permutable embeddings of subgroups of finite groups
Adolfo
Ballester-Bolinches
Universitat de València, BURJASSOT (VALENCIA), SPAIN
James
Beidleman
University of Kentucky, LEXINGTON, UNITED STATES
Finite group, permutability, S-permutability, S-semipermutability
In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied.
Group theory and generalizations
339
347
10.4171/RLM/766
http://www.ems-ph.org/doi/10.4171/RLM/766
Modular interpolation and modular estimates of the Fourier transform and related operators
Kwok-Pun
Ho
The Education University of Hong Kong, HONG KONG, CHINA
Modular inequality, Fourier transform, interpolation, Hankel transform, oscillatory integrals, Fourier restriction
We introduce an approach to modular interpolation in this paper. By using this interpolation, we establish the modular inequalities for the Fourier transform, the Laplace transform, the Hankel transform and the oscillatory integral operators. Moreover, we also obtain the modular Fourier restriction theorem.
Fourier analysis
Functional analysis
349
368
10.4171/RLM/767
http://www.ems-ph.org/doi/10.4171/RLM/767
On the approximation of SBV functions
Guido
De Philippis
SISSA, TRIESTE, ITALY
Nicola
Fusco
Università degli Studi di Napoli Federico II, NAPOLI, ITALY
Aldo
Pratelli
Universität Erlangen-Nürnberg, ERLANGEN, GERMANY
SBV functions, approximation, free discontinuity problems
In this paper we deal with the approximation of SBV functions in the strong BV topology. In particular, we provide three approximation results. The first one, Theorem A, concerns general SBV functions; the second one, Theorem B, concerns SBV functions with absolutely continuous part of the gradient in $L^p$, $p>1$; and the third one, Theorem C, concerns SBV$^p$ functions, that is, those SBV functions for which not only the absolutely continuous part of the gradient is in $L^p$, but also the jump set has finite $\mathcal H^{N-1}$-measure. The last result generalizes the previously known approximation theorems for\SBV$^p$ functions, see [5, 7]. As we discuss, the first and the third result are sharp. We conclude with a simple application of our results.
Real functions
369
413
10.4171/RLM/768
http://www.ems-ph.org/doi/10.4171/RLM/768