location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword Lipschitz

 Expand all        Collapse all Results 1 - 4 of 4

1. CJM Online first

Ostrovskii, Mikhail; Randrianantoanina, Beata
 Metric spaces admitting low-distortion embeddings into all $n$-dimensional Banach spaces For a fixed $K\gg 1$ and $n\in\mathbb{N}$, $n\gg 1$, we study metric spaces which admit embeddings with distortion $\le K$ into each $n$-dimensional Banach space. Classical examples include spaces embeddable into $\log n$-dimensional Euclidean spaces, and equilateral spaces. We prove that good embeddability properties are preserved under the operation of metric composition of metric spaces. In particular, we prove that $n$-point ultrametrics can be embedded with uniformly bounded distortions into arbitrary Banach spaces of dimension $\log n$. The main result of the paper is a new example of a family of finite metric spaces which are not metric compositions of classical examples and which do embed with uniformly bounded distortion into any Banach space of dimension $n$. This partially answers a question of G. Schechtman. Keywords:basis constant, bilipschitz embedding, diamond graph, distortion, equilateral set, ultrametricCategories:46B85, 05C12, 30L05, 46B15, 52A21

2. CJM 2012 (vol 65 pp. 702)

Taylor, Michael
 Regularity of Standing Waves on Lipschitz Domains We analyze the regularity of standing wave solutions to nonlinear SchrÃ¶dinger equations of power type on bounded domains, concentrating on Lipschitz domains. We establish optimal regularity results in this setting, in Besov spaces and in HÃ¶lder spaces. Keywords:standing waves, elliptic regularity, Lipschitz domainCategories:35J25, 35J65

3. CJM 2006 (vol 58 pp. 64)

Filippakis, Michael; Gasiński, Leszek; Papageorgiou, Nikolaos S.
 Multiplicity Results for Nonlinear Neumann Problems In this paper we study nonlinear elliptic problems of Neumann type driven by the $p$-Laplac\-ian differential operator. We look for situations guaranteeing the existence of multiple solutions. First we study problems which are strongly resonant at infinity at the first (zero) eigenvalue. We prove five multiplicity results, four for problems with nonsmooth potential and one for problems with a $C^1$-potential. In the last part, for nonsmooth problems in which the potential eventually exhibits a strict super-$p$-growth under a symmetry condition, we prove the existence of infinitely many pairs of nontrivial solutions. Our approach is variational based on the critical point theory for nonsmooth functionals. Also we present some results concerning the first two elements of the spectrum of the negative $p$-Laplacian with Neumann boundary condition. Keywords:Nonsmooth critical point theory, locally Lipschitz function,, Clarke subdifferential, Neumann problem, strong resonance,, second deformation theorem, nonsmooth symmetric mountain pass theorem,, $p$-LaplacianCategories:35J20, 35J60, 35J85

4. CJM 2004 (vol 56 pp. 655)

Tao, Xiangxing; Wang, Henggeng
 On the Neumann Problem for the SchrÃ¶dinger Equations with Singular Potentials in Lipschitz Domains We consider the Neumann problem for the Schr\"odinger equations $-\Delta u+Vu=0$, with singular nonnegative potentials $V$ belonging to the reverse H\"older class $\B_n$, in a connected Lipschitz domain $\Omega\subset\mathbf{R}^n$. Given boundary data $g$ in $H^p$ or $L^p$ for $1-\epsilon Keywords:Neumann problem, SchrÃ¶dinger equation, Lipschitz, domain, reverse HÃ¶lder class,$H^p\$ spaceCategories:42B20, 35J10
 top of page | contact us | privacy | site map |