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European Mathematical Society Publishing House
2024-03-28 16:46:22
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RLM&vol=19&iss=3&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)
19
2008
3
Positive solutions of the Robin problem for semilinear elliptic equations on annuli
Yu-xia
Fu
Hunan University, CHANGSA HUNAN, CHINA
Qiuyi
Dai
Hunan University, CHANGSA HUNAN, CHINA
Positive solutions, Robin problem, semilinear elliptic equations
Partial differential equations
General
175
188
10.4171/RLM/516
http://www.ems-ph.org/doi/10.4171/RLM/516
Hardy–Sobolev inequalities and hyperbolic symmetry
Daniele
Castorina
Università di Roma Tor Vergata, ROMA, ITALY
Isabella
Fabbri
Università degli studi Roma Tre, ROMA, ITALY
Giovanni
Mancini
Università degli studi Roma Tre, ROMA, ITALY
Kunnath
Sandeep
Sharadanagar, BANGALORE, INDIA
Nonlinear PDE, hyperbolic symmetry; Hardy–Sobolev inequalities
We discuss uniqueness and nondegeneracy of extremals for some wheighted Sobolev inequalities and give some applications to Grushin and scalar curvature type equations. The main theme is hyperbolic symmetry.
Partial differential equations
General
189
197
10.4171/RLM/517
http://www.ems-ph.org/doi/10.4171/RLM/517
Transversality of equivariant mappings with closed associated differential forms on G-manifolds
Marc
Lesimple
Università di Padova, PADOVA, ITALY
Tullio
Valent
Università di Padova, PADOVA, ITALY
Perturbation problems, equivariant mappings, transversality
It is proved that any equivariant mapping between G-manifolds (G a Lie group), with a closed associated differential form, is transversal to the orbit of any point in its image up to a G-invariant subspace of the tangent space.
Global analysis, analysis on manifolds
Topological groups, Lie groups
Operator theory
Manifolds and cell complexes
199
204
10.4171/RLM/518
http://www.ems-ph.org/doi/10.4171/RLM/518
Axial impact on a semi-infinite elastic rod
Piero
Villaggio
Università di Pisa, PISA, ITALY
Elastic impact rod theory, energy method
An approximate theory for treating the axial collision of a rigid mass against an elastic rod was proposed by Saint–Venant more than 150 years ago. The method works only for short bars, under the assumption that the elastic axial displacement instantaneously propagates from one end to the other after the impact. Moreover, this hypothesis is unrealistic for long rods. Here we suggest an extension of the method which is able to treat the axial impact on the initial cross-section of a semi-infinite rod.
Mechanics of deformable solids
Partial differential equations
General
205
210
10.4171/RLM/519
http://www.ems-ph.org/doi/10.4171/RLM/519
Positive solutions of nonlinear Schrödinger–Poisson systems with radial potentials vanishing at infinity
Carlo
Mercuri
SISSA, TRIESTE, ITALY
Nonlinear Schrödinger equations, weighted Sobolev spaces, Pohozaev identity, Palais–Smale condition
We deal with a weighted nonlinear Schrödinger–Poisson system, allowing the potentials to vanish at infinity.
Partial differential equations
General
211
227
10.4171/RLM/520
http://www.ems-ph.org/doi/10.4171/RLM/520
An explicit lower bound for the block complexity of an algebraic number
Yann
Bugeaud
Université de Strasbourg, STRASBOURG CEDEX, FRANCE
Transcendence, Schmidt Subspace Theorem, combinatorics on words
Let $b \ge 2$ be an integer and $\xi$ be an irrational real number. Among other results, we establish an explicit lower bound for the number of distinct blocks of $n$ digits occurring in the $b$-ary expansion of $\xi$.
Number theory
General
229
235
10.4171/RLM/521
http://www.ems-ph.org/doi/10.4171/RLM/521
Uniqueness of signed measures solving the continuity equation for Osgood vector fields
Luigi
Ambrosio
Scuola Normale Superiore, PISA, ITALY
Patrick
Bernard
Université de Paris Dauphine, PARIS CEDEX 16, FRANCE
Continuity equation, Osgood vector fields, decomposition of currents
Nonnegative measure-valued solutions of the continuity equation are uniquely determined by their initial condition, if the characteristic ODE associated to the velocity field has a unique solution. In this paper we give a partial extension of this result to signed measure-valued solutions, under a quantitative two-sided Osgood condition on the velocity field. Our results extend those obtained for log-Lipschitz vector fields in \cite{BC}
Measure and integration
Partial differential equations
General
237
245
10.4171/RLM/522
http://www.ems-ph.org/doi/10.4171/RLM/522
On the martingale problem associated to the 2D and 3D stochastic Navier–Stokes equations
Giuseppe
Da Prato
Scuola Normale Superiore, PISA, ITALY
Arnaud
Debussche
Antenne de Bretagne, BRUZ, FRANCE
Stochastic Navier–Stokes, Kolmogorov equations, martingale problems, weak uniqueness
In this paper we consider a Markov semigroup $(P_t)_{t\ge 0}$ associated to $2D$ and $3D$ Navier-Stokes equations. In the two-dimensional case $P_t$ is unique, whereas in the three-dimensional case (where uniqueness is not known) it is constructed as in \cite{DPD-NS3D} and \cite{DO06}. For $d=2$, we explicit a core, identify the abstract generator of $(P_t)_{t\ge 0}$ with the differential Kolmogorov operator $L$ on this core and prove existence and uniqueness for the corresponding martingale problem. In dimension $3$, we are not able to prove a similar result and we explain the difficulties encountered. Nonetheless, we explicit a core for the generator of the transformed semigroup $(S_t)_{t\ge 0},$ obtained by adding a suitable potential and then using the Feynman--Kac formula. Then we identify the abstract generator $(S_t)_{t\ge 0}$ with a differential operator $N$ on this core and prove uniqueness for the stopped martingale problem.
Probability theory and stochastic processes
Dynamical systems and ergodic theory
Fluid mechanics
General
247
264
10.4171/RLM/523
http://www.ems-ph.org/doi/10.4171/RLM/523