1. CJM 2016 (vol 68 pp. 876)
 Ostrovskii, Mikhail; Randrianantoanina, Beata

Metric Spaces Admitting Lowdistortion 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, ultrametric Categories: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 domain Categories: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,, $p$Laplacian Categories: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, $H^p$ space Categories:42B20, 35J10 
