1. CJM 2013 (vol 66 pp. 429)
 RiveraNoriega, Jorge

Perturbation and Solvability of Initial $L^p$ Dirichlet Problems for Parabolic Equations over Noncylindrical Domains
For parabolic linear operators $L$ of second order in divergence form,
we prove that the solvability of initial $L^p$ Dirichlet problems for
the whole range $1\lt p\lt \infty$ is preserved under appropriate small
perturbations of the coefficients of the operators involved.
We also prove that if the coefficients of $L$ satisfy a suitable
controlled oscillation in the form of Carleson measure conditions,
then for certain values of $p\gt 1$, the initial $L^p$ Dirichlet problem
associated to $Lu=0$ over noncylindrical domains is solvable.
The results are adequate adaptations of the corresponding results for
elliptic equations.
Keywords:initial $L^p$ Dirichlet problem, second order parabolic equations in divergence form, noncylindrical domains, reverse HÃ¶lder inequalities Category:35K20 

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. 492)
 Chua, SengKee

Extension Theorems on Weighted Sobolev Spaces and Some Applications
We extend the extension theorems to weighted Sobolev spaces
$L^p_{w,k}(\mathcal D)$ on $(\varepsilon,\delta)$ domains with doubling weight $w$
that satisfies a Poincar\'e inequality and such that $w^{1/p}$ is locally
$L^{p'}$. We also make use of the main theorem to improve weighted
Sobolev interpolation inequalities.
Keywords:PoincarÃ© inequalities, $A_p$ weights, doubling weights, $(\ep,\delta)$ domain, $(\ep,\infty)$ domain Category:46E35 

4. CJM 2006 (vol 58 pp. 401)
 Kolountzakis, Mihail N.; Révész, Szilárd Gy.

On Pointwise Estimates of Positive Definite Functions With Given Support
The following problem has been suggested by Paul Tur\' an. Let
$\Omega$ be a symmetric convex body in the Euclidean space $\mathbb R^d$
or in the torus $\TT^d$. Then, what is the largest possible value
of the integral of positive definite functions that are supported
in $\Omega$ and normalized with the value $1$ at the origin? From
this, Arestov, Berdysheva and Berens arrived at the analogous
pointwise extremal problem for intervals in $\RR$. That is, under
the same conditions and normalizations, the supremum of possible
function values at $z$ is to be found for any given point
$z\in\Omega$. However, it turns out that the problem for the real
line has already been solved by Boas and Kac, who gave several
proofs and also mentioned possible extensions to $\RR^d$ and to
nonconvex domains as well.
Here we present another approach to the problem, giving the
solution in $\RR^d$ and for several cases in~$\TT^d$. Actually, we
elaborate on the fact that the problem is essentially
onedimensional and investigate nonconvex open domains as well.
We show that the extremal problems are equivalent to some more
familiar ones concerning trigonometric polynomials, and thus find
the extremal values for a few cases. An analysis of the
relationship between the problem for $\RR^d$ and that for $\TT^d$
is given, showing that the former case is just the limiting case
of the latter. Thus the hierarchy of difficulty is established, so
that extremal problems for trigonometric polynomials gain renewed
recognition.
Keywords:Fourier transform, positive definite functions and measures, TurÃ¡n's extremal problem, convex symmetric domains, positive trigonometric polynomials, dual extremal problems Categories:42B10, 26D15, 42A82, 42A05 

5. 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 

6. CJM 2002 (vol 54 pp. 1121)
 Bao, Jiguang

Fully Nonlinear Elliptic Equations on General Domains
By means of the Pucci operator, we construct a function $u_0$, which plays
an essential role in our considerations, and give the existence and regularity
theorems for the bounded viscosity solutions of the generalized Dirichlet
problems of second order fully nonlinear elliptic equations on the general
bounded domains, which may be irregular. The approximation method, the accretive
operator technique and the Caffarelli's perturbation theory are used.
Keywords:Pucci operator, viscosity solution, existence, $C^{2,\psi}$ regularity, Dini condition, fully nonlinear equation, general domain, accretive operator, approximation lemma Categories:35D05, 35D10, 35J60, 35J67 
