- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 15:07:14
19
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RMI&vol=16&update_since=2024-03-28
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
16
2000
1
On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations
Marco
Cannone
Université Paris 7, PARIS CEDEX 05, FRANCE
Fabrice
Planchon
Institut Galilée, Université Paris 13, VILLETANEUSE, FRANCE
We derive various estimates for strong solutions to the Navier- Stokes equations in $C(|0,T)$, $L^3 (\mathbb R^3)$ that allow us to prove some regularity results on the kinematic bilinear term.
General
1
16
10.4171/RMI/268
http://www.ems-ph.org/doi/10.4171/RMI/268
Superharmonicity of nonlinear ground states
Peter
Lindqvist
Norwegian University of Science and Technology, TRONDHEIM, NORWAY
Juan
Manfredi
University of Pittsburgh, PITTSBURGH, UNITED STATES
Eero
Saksmann
University of Helsinki, HELSINKI, FINLAND
General
17
28
10.4171/RMI/269
http://www.ems-ph.org/doi/10.4171/RMI/269
Global orthogonality implies local almost-orthogonality
J. Michael
Wilson
The University of Vermont, BURLINGTON, UNITED STATES
We introduce a new stopping- time argument adapted to handle linear sums of noncompactly- supported functions that satisfy fairly weak decay smoothness and cancellation conditions. We use the argument to obtain a new Littlewood- Paley- type result for such sums.
General
29
48
10.4171/RMI/270
http://www.ems-ph.org/doi/10.4171/RMI/270
A geometric classification of Lie groups
Pierre
Charollois
Université Paris 6 Pierre et Marie Curie, PARIS CEDEX 05, FRANCE
General
49
136
10.4171/RMI/271
http://www.ems-ph.org/doi/10.4171/RMI/271
Removable sets for Lipschitz harmonic functions in the plane
Guy
David
Université Paris-Sud, ORSAY CEDEX, FRANCE
Pertti
Mattila
University of Helsinki, HELSINKI, FINLAND
General
137
215
10.4171/RMI/272
http://www.ems-ph.org/doi/10.4171/RMI/272
Corrigenda: Singular integral operators with non-smooth kernels on irregular domains
Xuan Thinh
Duong
Macquarie University, SYDNEY, NSW, AUSTRALIA
Alan
McIntosh
Australian National University, CANBERRA, AUSTRALIA
General
217
217
10.4171/RMI/273
http://www.ems-ph.org/doi/10.4171/RMI/273
2
Pseudo differential operators with negative definite symbols of variable order
Walter
Hoh
Universität Bielefeld, BIELEFELD, GERMANY
General
219
241
10.4171/RMI/274
http://www.ems-ph.org/doi/10.4171/RMI/274
Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
Nageswari
Shanmugalingam
University of Cincinnati, CINCINNATI, UNITED STATES
This paper studies a possible de finition of Sobolev spaces in abstract metric spaces and answers in the affi rmative the question whether this defi nition yields a Banach space. The paper also explores the relationship between this defi nition and the Haj lasz spaces. For specialized metric spaces the Sobolev embedding theorems are proven . Diff erent versions of capacities are also explored and these various def initions are compared. The main tool used in this paper is the concept of moduli of path families .
General
243
279
10.4171/RMI/275
http://www.ems-ph.org/doi/10.4171/RMI/275
Evolution d'une singularité de type cusp dans une poche de tourbillon
Raphaël
Danchin
Université Paris 12 – Val de Marne, CRÉTEIL CEDEX, FRANCE
Dans cet article on étudie l'évolution de singularités dans la frontière de poches de tourbillon pour les équations de la m écanique des fl uides incompressible en dimension deux. On s' intéresse en particulier aux singularit es de type cusp qui, d 'après des simulations numériques réecentes, semblent stables. On prouve ici que le champ de vitesse engendré par une poche de tourbillon ayant un cusp est lipschitzien (ce qui n'est pas le cas pour une singularité de type coin par exemple). On établit alors un r ésultat de persistance globale en temps d' un certain type de r egularité conormale du tourbillon par rapport à une famille de champs de vecteurs s' annulant en un point singulier et qui généralise la structure de cusp. On en déduit en particulier la stabilit é pour tout temps du cusp avec conservation de l' ordre d' effi lement.
General
281
329
10.4171/RMI/276
http://www.ems-ph.org/doi/10.4171/RMI/276
Construction of functions with prescribed Hölder and chirp exponents
Stéphane
Jaffard
Université Paris Est, CRÉTEIL CEDEX, FRANCE
We show that the H ölder exponent and the chirp exponent of a function can be prescribed simultaneously on a set of full measure , if they are both lower limits of continuous functions. We also show that this result is optimal: In general H ölder and chirp exponents cannot be prescribed outside a set of Hausdorff dimension less than one. The direct part of the proof consists in an explicit construction of a function determined by its orthonormal wavelet coeffi cients; the optimality is the direct consequence of a general method we introduce in order to obtain lower bounds on the dimension of some fractal sets .
General
331
349
10.4171/RMI/277
http://www.ems-ph.org/doi/10.4171/RMI/277
On nonisometric isospectral connected fractal domains
Brian
Sleeman
University of Leeds, LEEDS, UNITED KINGDOM
Hua
Chen
Wuhan University, WUHAN, HUBEI, CHINA
A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but nonisometric. In this note we study the Kac question in relation to domains with fractal boundaries and by following a technique of paper folding maps by J. Chapman 1993 we construct pairs of isospectral but nonisometric connected planar domains with fractal boundaries having the same Minkowski dimension.
General
351
361
10.4171/RMI/278
http://www.ems-ph.org/doi/10.4171/RMI/278
Measure-preserving quality within mappings
Stephen
Semmes
Rice University, HOUSTON, UNITED STATES
In [6] Guy David introduced some methods for finding controlled behavior in Lipschitz mappings with substantial images( in terms of measure). Under suitable conditions, David produces subsets on which the given mapping is bilipschitz with uniform bounds for the bilipschitz constant and the size of the subset. This has applications for boundedness of singular integral operators and "uniform rectifi ability" of sets as in [6, 7, 11, 13]. Some special cases of David s results , concerning projections of subsets of Euclidean spaces of codimension 1, or mappings defi ned on Euclidean spaces ( rather than sets or met ric spaces of less simple nature), have been given alternate and much simpler proofs, as in [8, 9, 10]. In general this has not occurred. Here we shall present a variation on David' s method which breaks down into simpler pieces. We shall also take advantage of some com ponents of the work of Peter Jones [19]. Jones' approach uses some Littlewood -Paley theory , and one of the important features of David 's method was to avoid this, operating in a more directly geometric way which could be applied more broadly. To some extent the present organization gives a reconciliation between the two, and between David' s stopping- time argument and techniques related to Carleson measures and Carleson' s Corona construction. In general this has not occurred Here we shall present a variation on David s method which breaks down into simpler pieces We shall also take advantage of some com ponents of the work of Peter Jones Jones approach uses some Littlewood Paley theory and one of the important features of David s method was to avoid this operating in a more directly geometric way which could be applied more broadly To some extent the present or ganization gives a reconciliation between the two and between David s stopping time argument and techniques related to Carleson measures and Carleson s Corona construction Some special cases of David s results concerning projections of subsets of Euclidean spaces of codimension or mappings de ned on Euclidean spaces rather than sets or met ric spaces of less simple nature have been given alternate and much simpler proofs as in In general this has not occurred Here we shall present a variation on David s method which breaks down into simpler pieces We shall also take advantage of some com ponents of the work of Peter Jones Jones approach uses some Littlewood Paley theory and one of the important features of David s method was to avoid this operating in a more directly geometric way which could be applied more broadly To some extent the present or ganization gives a reconciliation between the two and between David s stopping time argument and techniques related to Carleson measures and Carleson s Corona construction
General
363
458
10.4171/RMI/279
http://www.ems-ph.org/doi/10.4171/RMI/279
3
On the generalized Bernoulli numbers that belong to unequal characters
Ilya
Slavutskii
, JERUSALEM, ISRAEL
The study of class number invariants of absolute abelian fi elds, the investigation of congruences for special values of $L$- functions, Fourier coeffi cients of half- integral weight modular forms Rubin 's congruences involving the special values of $L$- functions of elliptic curves with complex multiplication, and many other problems require congruence properties of the generalized Bernoulli numbers ( see [16-18, 12, 29, 3], etc.) The rst steps in this direction can be found in the papers of H W Leopoldt (see [15]) and L Carlitz ( see [5]). For further studies see [22, 24, 29]. This paper presents some new examples extending both old author 's results and recent investigations of H Lang ( see [14]), A Balog, H Darmon, K Ono (see [3]), etc. On the whole the proved results are consequence of congruences connecting the generalized Bernoulli numbers that belong to unequal characters. This paper presents some new examples ex tending both old author s results and recent investigations of H Lang see A Balog H Darmon K Ono see etc On the whole the proved results are consequence of congruences connecting the generalized Bernoulli numbers that belong to unequal characters etc The rst steps in this direction can be found in the papers of H W Leopoldt see and L Carlitz see For further studies see This paper presents some new examples ex tending both old author s results and recent investigations of H Lang see A Balog H Darmon K Ono see etc On the whole the proved results are consequence of congruences connecting the generalized Bernoulli numbers that belong to unequal characters
General
459
475
10.4171/RMI/280
http://www.ems-ph.org/doi/10.4171/RMI/280
An elliptic semilinear equation with source term involving boundary measures: the subcritical case
Marie-Françoise
Bidaut-Véron
Université de Tours, TOURS, FRANCE
Laurent
Vivier
Université de Toulon et du Var, LA GARDE CEDEX, FRANCE
We study the boundary behaviour of the nonnegative solu tions of the semilinear elliptic equation in a bounded regular domain $\Omega$ of $\mathbb R^N (N≥2)$, $${\Delta u+u^q = 0}, in \Omega$$ $$u=\mu, on \partial \Omega$$, where $1 < q < (N+1) / (N-1)$ and $\mu$ is a Radon measure on $\partial \Omega$. We give a priori estimates and existence results. They lie on the study of the superharmonic functions in some weighted Marcinkiewicz spaces.
General
477
513
10.4171/RMI/281
http://www.ems-ph.org/doi/10.4171/RMI/281
On ovals on Riemann surfaces
Grzegorz
Gromadzki
University of Gdańsk, GDAŃSK, POLAND
We prove that $k (k ≥ 9)$ non -conjugate symmetries of a Riemann surface of genus $g$ have at most $2g-2+2^{r-3}(9-k)$ ovals in total, where $r$ is the smallest positive integer for which $k≤2^{r-1}$. Furthermore we prove that for arbitrary $k≥9$ this bound is sharp for infinitely many values of $g$.
General
515
527
10.4171/RMI/282
http://www.ems-ph.org/doi/10.4171/RMI/282
Schiffer problem and isoparametric hypersurfaces
Vladimir
Shklover
University of Maryland, COLLEGE PARK, UNITED STATES
The Schi ffer Problem as originally stated for Euclidean spaces ( and later for some symmetric spaces) is the following: Given a bounded connected open set $\Omega$ with a regular boundary and such that the complement of its closure is connected, does the existence of a so lution to the Overdetermined Neumann Problem (N) imply that $\Omega$ is a ball? The same question for the Overdetermined Dirichlet Problem (D). We consider the generalization of the Schi ffer Problem to an ar bitrary Riemannian manifold and also the possibility of replacing the condition on the domain to be a ball by more general condition; to have a homogeneous boundary (i.e., boundary , admitting a transitive group of isometries ). We prove that if $\Omega$ has a homogeneous boundary then (N) and (D) always admit solutions ( in fact, for infi nitely many eigenvalues), but the converse statement is not always true. We show that in a number of spaces (symmetric and non symmetric), many domains such that their boundaries are isoparametric hypersurfaces have eigenfunctions for (N) and (D) but fail the Schi ffer Conjecture or even its generalization. These ideas can be extended to other (essentially more compli cated) overdetermined boundary value problems, including higher or der equations and non linear equations which, in a number of important cases, may also have solutions in domains with isoparamet ric ( and not necessarily homogeneous) boundaries. Also, a number of initial/ boundary value problems for time- dependent equations with some extra boundary conditions have solutions for domains with the above boundaries. If a time- dependent equation is non linear and has blow- up, this blow- up occurs at the same time at all the points on the boundary.
General
529
569
10.4171/RMI/283
http://www.ems-ph.org/doi/10.4171/RMI/283
Jacobi-Eisenstein series of degree two over Cayley numbers
Minking
Eie
National Chung Cheng University, CHIA-YI, TAIWAN
We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi Eisenstein series which forms the orthogonal complement of the vector space of Jacobi cusp forms of degree two over Cayley numbers . The construction is based on a group representation arising from the trans formation formula of a set of theta series .
General
571
596
10.4171/RMI/284
http://www.ems-ph.org/doi/10.4171/RMI/284
Spectral multipliers on metabelian groups
Waldemar
Hebisch
Uniwersytet Wrocławski, WROCLAW, POLAND
General
597
604
10.4171/RMI/285
http://www.ems-ph.org/doi/10.4171/RMI/285
Unicité dans $L^3 (\mathbb R^3)$ et d'autres espaces fonctionnels limites pour Navier-Stokes
Giulia
Furioli
Università di Bergamo, DALMINE, ITALY
Pierre Gilles
Lemarié-Rieusset
Université d'Évry Val d'Essonne, EVRY CEDEX, FRANCE
Elide
Terraneo
Università degli Studi di Milano, MILANO, ITALY
The main result of this paper is the proof of uniqueness for mild solutions of the Navier- Stokes equations in $L^3 (\mathbb R^3)$. This result is extended as well to some Morrey- Campanato spaces.
General
605
667
10.4171/RMI/286
http://www.ems-ph.org/doi/10.4171/RMI/286