- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 06:50:19
9
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RMI&vol=3&iss=3&update_since=2024-03-29
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)
3
1987
3
The Relation Between the Porous Medium and the Eikonal Equations in Several Space Dimensions
Pierre-Louis
Lions
Univ de Paris IX Dauphine, PARIS CEDEX 05, FRANCE
Panagiotis
Souganidis
Brown University, PROVIDENCE, UNITED STATES
Juan Luis
Vázquez
Universidad Autónoma de Madrid, MADRID, SPAIN
We study the relation between the porous medium equation $u_t = \Delta(u^m), \; m>1$, and the eikonal equation $\nu_t = |D\nu|^2$. Under quite general assumptions, we prove that the pressure and the interface of the solution of the Cauchy problem for the porous medium equation converge as $m \downarrow 1$ to the viscosity solution and the interface of the Cauchy problem for the eikonal equation. We also address the same questions for the case of the Dirichlet boundary value problem.
General
275
310
10.4171/RMI/51
http://www.ems-ph.org/doi/10.4171/RMI/51
Norm Inequalities for Potential-Type Operators
Sagun
Chanillo
Rutgers University, PISCATAWAY, UNITED STATES
Jan-Olov
Strömberg
Trømso Universitet, TROMSO, NORWAY
Richard
Wheeden
Rutgers University, NEW BRUNSWICK, UNITED STATES
General
311
335
10.4171/RMI/52
http://www.ems-ph.org/doi/10.4171/RMI/52
Structural Stability and Generic Properties of Planar Polynomial Vector Fields
Douglas
Shafer
University of North Carolina-Charlotte, CHARLOTTE, UNITED STATES
General
337
355
10.4171/RMI/53
http://www.ems-ph.org/doi/10.4171/RMI/53
On the Spaces of Eisenstein Series of Hilbert Modular Groups
Toshitsune
Miyake
Hokkaido University, SAPPORO, JAPAN
General
357
369
10.4171/RMI/54
http://www.ems-ph.org/doi/10.4171/RMI/54
Eigenvalue Problems of Quasilinear Elliptic Systems on $R^n$
Gongbao
Li
Huazhong Normal University, WUHAN, CHINA
In this paper, we get the existence results of the nontrivial weak solution $(\lambda, u)$ of the following eigenvalue problem of quasilinear elliptic systems $$–D_\alpha (a_{\alpha \beta}(x, u)D_\beta u^i) + \frac{1}{2}D_{u^i}a_{\alpha \beta}(x, u)D_\alpha u^jD_\beta u^j + h(x)u^i = \lambda |u|^{p–2}u^i,$$ for $x \in \mathbb R^n$, $1 ≤ i ≤ N$ and $$u = (u^1, u^2, ..., u^N) \in E = \{ \nu = (\nu^1, \nu^2, ..., \nu^N) | \nu^i \in H^1 (\mathbb R^n), 1 ≤ i ≤ N \},$$ where $a_{\alpha \beta} (x, u)$ satisfy the natural growth conditions. It seems that this kind of problem has never been dealt with before.
General
371
399
10.4171/RMI/55
http://www.ems-ph.org/doi/10.4171/RMI/55
An Atomic Decomposition of the Predual of BMO$(\rho)$
Beatriz
Viviani
Universidad Nacional del Litoral, SANTA FÉ, ARGENTINA
We study the Orlicz type spaces $H_\omega$, defined as a generalization of the Hardy spaces $H^p$ for $p ≤ 1$. We obtain an atomic decomposition of $H_\omega$, which is used to provide another proof of the known fact that BMO$(\rho)$ is the dual space of $H_\omega$ (see S. Janson, 1980, [J]).
General
401
425
10.4171/RMI/56
http://www.ems-ph.org/doi/10.4171/RMI/56
Global Models of Riemannian Metrics
J.
Fontanillas
Universidad Autónoma de Madrid, MADRID, SPAIN
F.
Varela
Universidad Autónoma de Madrid, MADRID, SPAIN
General
427
445
10.4171/RMI/57
http://www.ems-ph.org/doi/10.4171/RMI/57
Compact Hypersurfaces with Constant Higher Order Mean Curvatures
Antonio
Ros
Universidad de Granada, GRANADA, SPAIN
General
447
453
10.4171/RMI/58
http://www.ems-ph.org/doi/10.4171/RMI/58
Oblique Derivative Problems for the Laplacian in Lipschitz Domains
Jill
Pipher
Brown University, PROVIDENCE, UNITED STATES
General
455
472
10.4171/RMI/59
http://www.ems-ph.org/doi/10.4171/RMI/59