Bulletin Des Sciences Mathematiques 

About: Bulletin Des Sciences Mathematiques is an academic journal published by Elsevier BV. The journal publishes majorly in the area(s): Mathematics & Bounded function. It has an ISSN identifier of 0007-4497. Over the lifetime, 1389 publications have been published receiving 20746 citations. The journal is also known as: Bibliothèque de l'École des hautes études. Bulletin des sciences mathématiques.

Hitchhiker's guide to the fractional Sobolev spaces

Abstract: This paper deals with the fractional Sobolev spaces W s;p . We analyze the relations among some of their possible denitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results. Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains.

Maximal function on Musielak–Orlicz spaces and generalized Lebesgue spaces

Abstract: We consider the Hardy–Littlewood maximal operator M on Musielak–Orlicz Spaces L φ ( R d ) . We give a necessary condition for the continuity of M on L φ ( R d ) which generalizes the concept of Muckenhoupt classes. In the special case of generalized Lebesgue spaces L p ( ⋅ ) ( R d ) we show that this condition is also sufficient. Moreover, we show that the condition is “left-open” in the sense that not only M but also M q is continuous for some q > 1 , where M q f = ( M ( | f | q ) ) 1 q .

Averaging methods for finding periodic orbits via Brouwer degree

Abstract: We consider the problem of finding T -periodic solutions for a differential system whose vector field depend on a small parameter e. An answer to this problem can be given using the averaging method. Our main results are in this direction, but our approach is new. We use topological methods based on Brouwer degree theory to solve operator equations equivalent to this problem. The regularity assumptions are weaker then in the known results (up to second order in e). A result for third order averaging method is also given. As an application we provide a way to study bifurcations of limit cycles from the period annulus of a planar system and notice relations with the displacement function. A concrete example is given.  2003 Elsevier SAS. All rights reserved. MSC: 34C29; 34C25; 47H11

Hypersurfaces of constant curvature in space forms

Abstract: In this paper we shall discuss hypersurfaces M of space forms of constant curvature; where curvature means one of the symmetric functions of curvature associated to the second fundamental form. The values of the constant will be chosen so that the linearized equation will be an elliptic equation onM . For example, for surfaces in 3 the two possible curvatures are the mean curvature H and the Gaussian curvature K. The linearized equation for H is always elliptic and for K it is elliptic when the constant K is positive. In hyperbolic 3-space, the constant K > −1 yields an elliptic equation. Hypersurfaces of constant scalar curvature S2 will be elliptic when S2 > 0. We obtain height estimates for compact embedded hypersurfaces of m+1 whose r + 1’st symmetric function of curvature, Sr+1, is a positive constant (§6.1.): Given such a hypersurface M , with ∂M contained in a hyperplane P , then the maximum distance of a point of M to P is