bluuebunny/crossref_metadata_2025_split huggingface dataset:
The decay dynamics of photoexcited argon cluster ions
Authors: Smith J. A. , Gotts N. G. , Winkel J. F. , Hallett R. , Woodward C. A. , Stace A. J. , Whitaker B. J. 
Published: July 2002

Following the photoexcitation of argon cluster ions, Ar+n for n in the range 4–25, kinetic energy release measurements have been undertaken on the fragments using two quite separate techniques. For Ar+4–Ar+6, fragment ion kinetic energy spectra were recorded at 532 nm in a crossed beam apparatus as a function of the angle of polarization of the laser radiation with respect to the incident ion beam. Only Ar+ from Ar+4 was observed to exhibit a polarization dependence together with a comparatively high kinetic energy release. The principal fragment ion Ar+2 was found both to emerge with a low kinetic energy release and to display no dependence on the angle of polarization of the radiation. In a second series of experiments, mass and kinetic energy resolved cluster ions were photodissociated in the entrance to a time-of-flight (TOF) device of variable length. The subsequent deflection of all ions allowed for time resolved measurements to be undertaken on the neutral photofragments. Following the absorption of a photon, all cluster ions up to Ar+25 were found to eject one/two neutral atoms with comparatively high kinetic energies. Any remaining internal energy appears to be dissipated through the loss of further neutral atoms with low kinetic energies. An analysis of the laser polarization dependence of these events, shows that those atoms identified as having high kinetic energies are ejected on a time scale which is short compared with the rotation period of a cluster (≂10 ps).
These experimental observations are consistent with the results of recent molecular dynamics simulations of excited states in rare gas clusters by Landman, Jortner, and co-workers [J. Phys. Chem. 91, 4890 (1987); J. Chem. Phys. 88, 4273 (1988)]. Kinetic energy releases calculated from the TOF spectra exhibit marked fluctuations as a function of cluster size, with Ar+15 showing a minimum and Ar+19 a maximum. It is suggested that such behavior is part of a dynamic response to changes in structure as the cluster ions increase in size. A qualitative explanation is provided through the assumption that the cluster ions take the form of solvated Ar+2 structures. Considerations of the energy available from the photon and the relative contribution each TOF feature makes to the total signal, places an upper limit of two as the number of high kinetic energy atoms ejected by the larger cluster ions.
Two nonlinear control schemes contrasted on a hydrodynamiclike model
Authors: Keefe Laurence R. 
Published: July 2002

The feasibility of shear flow control using strategies originated by Hübler (H), and by Ott, Grebogi, and Yorke (OGY), has been examined numerically employing fully developed and transitional solutions of the Ginzburg–Landau equation as models for such flows. The general message of this study is that control of nonlinear systems is best obtained by making maximum use possible of the underlying natural dynamics. The effectiveness of both methods in obtaining control of fully developed flows depends strongly upon the ‘‘distance’’ in state space between the uncontrolled flow and goal dynamics. If the goal dynamics is an unstable nonlinear solution of the equation, or a close approximation, and the flow is nearby at the instant control is applied, both methods perform reliably and at low-energy cost in reaching and maintaining this goal. For example, under conditions when the spatially complex and temporally chaotic uncontrolled flow exists on a strange attractor of Lyapunov dimension Dλ≂120, several different spatially periodic limit cycle motions (Dλ=1) were successfully maintained by both methods using less than 1% of the energy of the chaotic motion.
However, when the goal dynamics is not nearby the uncontrolled flow state at the instant control is attempted, both methods can fail in their own unique way. In the H method the failure occurs because multiple solutions of the forced equation result from the same forcing. This could be a generic problem in all nonlinear systems, the Navier–Stokes equations included. In some cases this failure may be avoided by defining and controlling to a sequence of intermediate goals that lead to the ultimate dynamics. This staged approach to a goal shows potential of helping the OGY method when it also fails. Here the ‘‘targeting’’ methods useful in low-dimensional systems for moving from uncontrolled states to a goal region fail because of the underlying complexity of the attractor, or because the goal dynamics are not embedded within the chaotic attractor of the uncontrolled system. There are conceptual difficulties in applying the OGY method to transitional, convectively unstable flows, but within certain limitations the H method works well, though at a large cost in energy terms. It works best when the goal dynamics rearranges the energy of the uncontrolled flow into new nonlinear forms, rather than simply trying to suppress it. The performance of both methods degrades due to noise and the spatially discrete nature of realistic forcing, but these effects are not difficult to predict. It is suggested that channel flows may be particularly amenable to control by either the H or OGY methods, while the H method seems more appropriate for boundary layers.
Effect of nicotinamide administration on ethanol consumption and on liver and brain acetaldehyde oxidation rate, by UChB rats
Authors: TAMPIER LUTSKE , QUINTANILLA MARÍA ELENA , MARDONES JORGE 
Published: July 2002

AbstractThe activities of liver and brain aldehyde dehydrogenase, an NAD+ dependent enzyme, which controls acetaldehyde oxidation have been reported to play a role in voluntary ethanol consumption. It has been reported that nicotinamide administration to rats increases NAD+ levels, that may increase acetaldehyde oxidation rates if basal NAD+ levels are not saturating for the enzyme. In the present paper the effect of nicotinamide administration on voluntary ethanol consumption by genetically high ethanol consumer UChB rats and brain and liver mitochondrial acetaldehyde oxidation were studied. Administration of nicotinamide 250 or 500 mg/kg i.p. to UChB rats, produced a significant reduction in their voluntary ethanol consumption and increased brain acetaldehyde oxidation in brain but not liver homogenates.These results suggest that basal NAD+ levels are not saturating for brain aldehyde dehydrogenase and that the reduction of ethanol consumption by UChB rats may be the consequence of a change in the brain redox state, rather than the local level of acetaldehyde.
Intrinsic Signals in the Unique Domain Target p56lckto the Plasma Membrane Independently of CD4
Authors: Bijlmakers Marie-José J.E. , Isobe-Nakamura Misako , Ruddock Lindsay J. , Marsh Mark 
Published: July 2002

In T lymphocytes, the Src-family protein tyrosine kinase p56lck (Lck) is mostly associated with the cytoplasmic face of the plasma membrane. To determine how this distribution is achieved, we analyzed the location of Lck in lymphoid and in transfected nonlymphoid cells by immunofluorescence. We found that in T cells Lck was targeted correctly, independently of the cell surface proteins CD4 and CD8 with which it interacts. Similarly, in transfected NIH-3T3 fibroblasts, Lck was localized at the plasma membrane, indicating that T cell–specific proteins are not required for targeting. Some variation in subcellular distribution was observed when Lck was expressed in HeLa and MDCK cells. In these cells, Lck associated with both the plasma membrane and the Golgi apparatus, while subsequent expression of CD4 resulted in the loss of Golgi-associated staining. Together, these data indicate that Lck contains intrinsic signals for targeting to the plasma membrane. Furthermore, delivery to this site may be achieved via association with exocytic transport vesicles.
A mutant Lck molecule in which the palmitoylation site at cysteine 5 was changed to lysine (LC2) localized to the plasma membrane and the Golgi region in NIH3T3 cells. However, the localization of a mutant in which the palmitoylation site at cysteine 3 was changed to serine (LC1) was indistinguishable from wild-type Lck. Chimeras composed of only the unique domain of Lck linked to either c-Src or the green fluorescent protein similarly localized to the plasma membrane of NIH-3T3 cells. Thus, the targeting of Lck appears to be determined primarily by its unique domain and may be influenced by the use of different palmitoylation sites.
Quadratic division algebras revisited (Remarks on an article by J. M. Osborn)
Authors: Dieterich Ernst 
Published: July 2002

In his remarkable article “Quadratic division algebras” (Trans. Amer. Math. Soc. 105 (1962), 202–221), J. M. Osborn claims to solve ‘the problem of determining all quadratic division algebras of order 4 over an arbitrary field

F
F

of characteristic not two

…
\ldots

modulo the theory of quadratic forms over

F
F

’ (cf. p. 206). While we shall explain in which respect he has not achieved this goal, we shall on the other hand complete Osborn’s basic results (by a reasoning which is finer than his) to derive in the real ground field case a classification of all 4-dimensional quadratic division algebras and the construction of a 49-parameter family of pairwise nonisomorphic 8-dimensional quadratic division algebras. To make these points clear, we begin by reformulating Osborn’s fundamental observations on quadratic algebras in categorical terms.
Convergence of paths for pseudo-contractive mappings in Banach spaces
Authors: Morales Claudio , Jung Jong 
Published: July 2002

Let

X
X

be a real Banach space, let

K
K

be a closed convex subset of

X
X

, and let

T
T

, from

K
K

into

X
X

, be a pseudo-contractive mapping (i.e.

(
λ
−
1
)

(\lambda -1)

‖
u
−
v
‖
≤
‖
(
λ
I
−
T
)
(
u
)
−
(
λ
I
−
T
)
(
v
)
‖

\|u-v\|\le \|(\lambda I-T)(u)-(\lambda I-T)(v)\|

for all

u
,
v
∈
K

u,v\in K

and

λ
>
1
)

\lambda >1)

. Suppose the space

X
X

has a uniformly Gâteaux differentiable norm, such that every closed bounded convex subset of

K
K

enjoys the Fixed Point Property for nonexpansive self-mappings. Then the path

t
→

x
t

∈
K

t\to x_t\in K

,

t
∈
[
0
,
1
)

t\in [0,1)

, defined by the equation

x
t

=
t
T

x
t

+
(
1
−
t
)

x
0

x_t=tTx_t+(1-t)x_0

is continuous and strongly converges to a fixed point of

T
T

as

t
→

1
−

t\to 1^-

, provided that

T
T

satisfies the weakly inward condition.
Solvability of a finite or infinite system of discontinuous quasimonotone differential equations
Authors: Biles Daniel , Schechter Eric 
Published: July 2002

This paper proves the existence of solutions to the initial value problem
\[

(

I
V
P

)

{

x
′

(
t
)
=
f
(
t
,
x
(
t
)
)

(
0
≤
t
≤
1
)
,
x
(
0
)
=
0
,

(\mathrm {IVP})\qquad \qquad \left \{\begin {array}{l} x’(t)=f(t,x(t))\qquad \quad (0\le t\le 1), x(0)=0,\end {array} \right .

\]
where

f
:
[
0
,
1
]
×

R

M

→

R

M

f:[0,1]\times \mathbb {R}^M\to \mathbb {R}^M

may be discontinuous but is assumed to satisfy conditions of superposition-measurability, quasimonotonicity, quasisemicontinuity, and integrability. The set

M
M

can be arbitrarily large (finite or infinite); our theorem is new even for

card

(
M
)
=
2

\mbox {card}(M)=2

. The proof is based partly on measure-theoretic techniques used in one dimension under slightly stronger hypotheses by Rzymowski and Walachowski. Further generalizations are mentioned at the end of the paper.
Borel complexity of the space of probability measures
Authors: Dasgupta Abhijit 
Published: July 2002

Using a technique developed by Louveau and Saint Raymond, we find the complexity of the space of probability measures in the Borel hierarchy: if

X
X

is any non-Polish Borel subspace of a Polish space, then

P
(
X
)

P(X)

, the space of probability Borel measures on

X
X

with the weak topology, is always true

Π

ξ

0

{\boldsymbol {\Pi }^{\boldsymbol {0}}_{\boldsymbol {\xi }}}

, where

ξ
\xi

is the least ordinal such that

X
X

is

Π

ξ

0

{\boldsymbol {\Pi }^{\boldsymbol {0}}_{\boldsymbol {\xi }}}

.
The Fefferman-Stein type inequality for the Kakeya maximal operator
Authors: Tanaka Hitoshi 
Published: July 2002

LetKδK_\delta,0>δ>>10>\delta >>1, be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricityδ\delta. We shall prove the so-called Fefferman-Stein type inequality forKδK_\delta,\[‖Kδf‖Lp(Rd,w)≤Cd,p(1δ)d/p−1(log⁡(1δ))α(d)‖f‖Lp(Rd,Kδw),\|K_\delta f\|_{L^p(\mathbf R^d,w)} \le C_{d,p} (\frac {1}{\delta })^{d/p-1} (\log (\frac {1}{\delta }))^{\alpha (d)} \|f\|_{L^p(\mathbf R^d,K_\delta w)},\]in the range(1>p≤(d2−2)/(2d−3)(1>p\le (d^2-2)/(2d-3),d≥3d\ge 3, with some constantsCd,pC_{d,p}andα(d)\alpha (d)independent offfand the weightww.
Iterative approximation of fixed points of Lipschitz pseudocontractive maps
Authors: Chidume C. 
Published: July 2002

Let

E
E

be a

q
q

-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g.,

ℓ
p

,

1
>
p
>
∞

\ell _p, \ 1>p>\infty

). Let

T
T

be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset

K
K

of

E
E

and let

ω
∈
K

\omega \in K

be arbitrary. Then the iteration sequence

{

z
n

}

\{z_n\}

defined by

z
0

∈
K
,

z

n
+
1

=
(
1
−

μ

n
+
1

)
ω
+

μ

n
+
1

y
n

;

y
n

=
(
1
−

α
n

)

z
n

+

α
n

T

z
n

z_0\in K, \ \ z_{n+1}=(1-\mu _{n+ 1})\omega + \mu _{n+1}y_n; \ \ y_n = (1-\alpha _n)z_n+\alpha _nTz_n

, converges strongly to a fixed point of

T
T

, provided that

{

μ
n

}

\{\mu _n\}

and

{

α
n

}

\{\alpha _n\}

have certain properties. If

E
E

is a Hilbert space, then

{

z
n

}

\{z_n\}

converges strongly to the unique fixed point of

T
T

closest to

ω
\omega

.
An application of Ramsey’s Theorem to the Banach Contraction Principle
Authors: Merryfield James , Rothschild Bruce , Stein James 
Published: July 2002

One of the most fundamental fixed-point theorems is Banach’s Contraction Principle, of which the following conjecture is a generalization. Generalized Banach Contraction Conjecture (GBCC). Let

T
T

be a self-map of a complete metric space

(
X
,
d
)

(X,d)

, and let

0
>
M
>
1

0>M>1

. Let

J
J

be a positive integer. Assume that for each pair

x
,
y
∈
X

x,y\in X

,

min
{
d
(

T
k

x
,

T
k

y
)
:
1
≤
k
≤
J
}
≤
M

d
(
x
,
y
)

\min \{d(T^kx, T^ky):1\le k\le J\}\le M\,d(x,y)

. Then

T
T

has a fixed point. Unlike Banach’s original theorem (the case

J
=
1

J=1

), the above hypothesis does not compel

T
T

to be continuous. In this paper we use Ramsey’s Theorem from combinatorics to establish the GBCC for arbitrary

J
J

in the case when

T
T

is assumed to be continuous, and also derive a result which enables us to prove the GBCC when

J
=
3

J=3

without the assumption of continuity; it is known that the case

J
=
3

J=3

includes instances where

T
T

is not continuous.
Simple algebras of Weyl type, II
Authors: Zhao Kaiming 
Published: July 2002

Over a field

F

\mathbb {F}

of any characteristic, for a commutative associative algebra

A
A

, and for a commutative subalgebra

D
D

of

Der

F

⁡
(
A
)

\operatorname {Der}_{\mathbb {F}}(A)

, the vector space

A
[
D
]

A[D]

which consists of polynomials of elements in

D
D

with coefficients in

A
A

and which is regarded as operators on

A
A

forms naturally an associative algebra. It is proved that, as an associative algebra,

A
[
D
]

A[D]

is simple if and only if

A
A

is

D
D

-simple. Suppose

A
A

is

D
D

-simple. Then, (a)

A
[
D
]

A[D]

is a free left

A
A

-module; (b) as a Lie algebra, the subquotient

[
A
[
D
]
,

A
[
D
]

]

/

(
Z
(
A
[
D
]
)
∩
[
A
[
D
]
,

A
[
D
]

]
)

[A[D],{A[D]}]/(Z(A[D])\cap [A[D], {A[D]}])

is simple (except for one case), where

Z
(
A
[
D
]
)

Z(A[D])

is the center of

A
[
D
]

A[D]

. The structure of this subquotient is explicitly described. This extends the results obtained by Su and Zhao.
Hölder estimates of solutions to a degenerate diffusion equation
Authors: Lu Yunguang 
Published: July 2002

This paper is concerned with the Hölder estimates of weak solutions of the Cauchy problem for the general degenerate parabolic equations

u

t

=
Δ
G
(
u
)
+

∑

j
=
1

N

f

j

(
u

)

x

j

+
h
(
u
)
,

\begin{equation*} u_{t}= \Delta G(u)+ \sum \limits _{j=1}^{N}f_{j}(u)_{x_{j}}+h(u), \end{equation*}

with the initial data

u
(
x
,
0
)
=

u

0

(

x
1

,

x
2

,
…
,

x
N

)

u(x,0)=u_{0}(x_1,x_2,\dots ,x_N)

, where the diffusion function

G
(
u
)

G(u)

can be a constant on a nonzero measure set, such as the equations of two-phase Stefan type. Some explicit Hölder exponents of the composition function

G
(
u
)

G(u)

with respect to the space variables are obtained by using the maximum principle.
Gaps in (𝒫(𝜔),⊂*) and (𝜔^{𝜔},≤*)
Authors: Spasojević Zoran 
Published: July 2002

For a partial order

(
P
,

≤
P

)

(P,\le _P)

, let

Γ
(
P
,

≤
P

)

\Gamma (P,\le _P)

denote the statement that for every

≤
P

\le _P

-increasing

ω
1

\omega _1

-sequence

a
⊆
P

a\subseteq P

there is a

≤
P

\le _P

-decreasing

ω
1

\omega _1

-sequence

b
⊆
P

b\subseteq P

on top of

a
a

such that

(
a
,
b
)

(a,b)

is an

(

ω
1

,

ω
1

)

(\omega _1,\omega _1)

-gap in

P
P

. The main result of this paper is that

t

>

ω
1

↔
Γ
(

P

(
ω
)
,

⊂
∗

)
↔
Γ
(

ω
ω

,

≤
∗

)

\mathfrak t>\omega _1\leftrightarrow \Gamma (\mathcal P(\omega ),\subset ^*)\leftrightarrow \Gamma (\omega ^\omega ,\le ^*)

. It is also shown, as a corollary, that

Γ
(

ω
ω

,

≤
∗

)
→

b

>

ω
1

\Gamma (\omega ^\omega ,\le ^*)\to \mathfrak b>\omega _1

but

b

>

ω
1

↛
Γ
(

ω
ω

,

≤
∗

)

\mathfrak b>\omega _1\not \to \Gamma (\omega ^\omega ,\le ^*)

.
Images of bilinear mappings into 𝐑³
Authors: Bernau S. , Wojciechowski Piotr 
Published: July 2002

It is well-known that the image of a multilinear mapping into a vector space need not be a subspace of its target space. It is, however, far from clear which subsets of the target space may be such images. For vector spaces over the real numbers we give a complete classification of the images of bilinear mappings into a three-dimensional vector space. In Theorem 2.8 we show that either the image of a bilinear mapping into a three-dimensional space is a subspace, or its complement is either the interior of a double elliptic cone, or a plane from which two lines intersecting at the origin have been removed. We also show (Theorem 2.2) that the image of any multilinear mapping into a two-dimensional space is necessarily a subspace. Our methods are elementary and free of tensor considerations.
Expanding the joint spectrum of pairs of commuting contractions
Authors: Ionescu Adrian 
Published: July 2002

We present a connection between solving the invariant subspace problem for a single operator

T
T

on Hilbert space and the existence of a common invariant subspace for two commuting related operators. In particular, we reduce the problem of the existence of nontrivial invariant subspaces for a single contraction with spectral radius one to the problem of the existence of common nontrivial invariant subspaces for a pair of commuting contractions with large joint spectra.
Duality and perfect probability spaces
Authors: Ramachandran D. , Rüschendorf L. 
Published: July 2002

Given probability spaces

(

X
i

,

A

i

,

P
i

)
,
i
=
1
,
2
,

(X_i,\mathcal {A}_i,P_i), i=1,2,

let

M

(

P
1

,

P
2

)

\mathcal {M}(P_1,P_2)

denote the set of all probabilities on the product space with marginals

P
1

P_1

and

P
2

P_2

and let

h
h

be a measurable function on

(

X
1

×

X
2

,

A

1

⊗

A

2

)
.

(X_1 \times X_2,\mathcal {A}_1 \otimes \mathcal {A}_2).

Continuous versions of linear programming stemming from the works of Monge (1781) and Kantorovich-Rubinštein (1958) for the case of compact metric spaces are concerned with the validity of the duality

a
m
p
;
sup
{
∫
h
d
P
:
P
∈

M

(

P
1

,

P
2

)
}

a
m
p
;

=

inf
{

∑

i
=
1

2

∫

h
i

d

P
i

:

h
i

∈

L

1

(

P
i

)

a
n
d

h
≤

⊕

i

h
i

}

\begin{align*} &\sup \{ \int h dP: P \in \mathcal {M}(P_1,P_2) \} \ &\qquad = \: \inf \{ \sum _{i=1}^{2} \int h_i dP_i : h_i \in \mathcal {L}^1 (P_i) \; \; and \; \; h \leq {\oplus }_i h_i\} \end{align*}

(where

M

(

P
1

,

P
2

)

\mathcal {M}(P_1,P_2)

is the collection of all probability measures on

(

X
1

×

X
2

,

A

1

⊗

A

2

)

(X_1 \times X_2, \mathcal {A}_1 \otimes \mathcal {A}_2)

with

P
1

P_1

and

P
2

P_2

as the marginals). A recently established general duality theorem asserts the validity of the above duality whenever at least one of the marginals is a perfect probability space. We pursue the converse direction to examine the interplay between the notions of duality and perfectness and obtain a new characterization of perfect probability spaces.
Generalized evaluation subgroups of product spaces relative to a factor
Authors: Lee Kee , Woo Moo 
Published: July 2002

For any

C
W

CW

-complexes

X
X

and

Y
Y

, we show that

G

n

(
X
×
Y
,
X
)
=

G

n

(
X
)
⊕

π

n

(
Y
)

G_{n}(X \times Y, X) = G_{n}(X) \oplus \pi _{n}(Y)

. We use this fact to compute generalized evaluation subgroups of generalized tori relative to a sphere.
The 𝐷-resultant, singularities and the degree of unfaithfulness
Authors: van den Essen Arno , Yu Jie-Tai 
Published: July 2002

We introduce the

D
D

-resultant of two polynomials in one variable and show how it can be used to decide if

k
(
f
(
t
)
,
g
(
t
)
)
=
k
(
t
)
,
k
[
f
(
t
)
,
g
(
t
)
]
=
k
[
t
]

k(f(t),g(t))=k(t),k[f(t),g(t)]=k[t]

and to find the singularities of the curve

x
=
f
(
t
)
,
y
=
g
(
t
)

x=f(t),y=g(t)

. The second criterion is used to give a very short proof of a special case of the epimorphism theorem of Abhyankar and Moh.
Wilson’s functional equation for vector and matrix functions
Authors: Sinopoulos Pavlos 
Published: July 2002

We determine the general solution of the functional equation
\[

f
(
x
+
y
)
+
f
(
x
−
y
)
=
A
(
y
)
f
(
x
)

(
x
,
y
∈
G
)
,

f(x+y)+f(x-y) =A(y)f(x)\qquad (x,y\in G),

\]
where

G
G

is a 2-divisible abelian group,

f
f

is a vector-valued function and

A
A

is a matrix-valued function. Using this result we solve the scalar equation
\[

f
(
x
+
y
)
+
f
(
x
−
y
)
=

g
1

(
x
)

h
1

(
y
)
+

g
2

(
x
)

h
2

(
y
)

(
x
,
y
∈
G
)
,

f(x+y)+f(x-y)=g_1(x)h_1(y)+g_2(x) h_2(y)\qquad (x,y\in G),

\]
which contains as special cases, among others, the d’Alembert and Wilson equations and the parallelogram law.
A new subcontinuum of 𝛽ℝ\ℝ
Authors: Dow Alan , Hart Klaas 
Published: July 2002

We present a method for describing all indecomposable subcontinua of

β

R

∖

R

\beta \mathbb {R}\setminus \mathbb {R}

. This method enables us to construct in

Z
F
C

\mathsf {ZFC}

a new subcontinuum of

β

R

∖

R

\beta \mathbb {R}\setminus \mathbb {R}

. We also show that the nontrivial layers of standard subcontinua can be described by our method. This allows us to construct a layer with a proper dense

F
σ

F_\sigma

-subset and bring the number of (known) nonhomeomorphic subcontinua of

β

R

∖

R

\beta \mathbb {R}\setminus \mathbb {R}

to 14.
A weighted Poincaré inequality with a doubling weight
Authors: Hurri-Syrjānen Ritva 
Published: July 2002

We show that unbounded John domains (and even a larger class of domains than John domains) satisfy the weighted Poincaré inequality

inf

a
∈

R

‖
u
(
x
)
−
a

‖

L

q

(
D
,

w

1

)

≤
C
‖
∇
u
(
x
)

‖

L

p

(
D
,

w

2

)

\begin{equation*}\inf _{a\in \mathbb {R}} \|u(x)-a\|_{L^{q}(D,w_{1})} \le C\|\nabla u(x)\|_{L^{p}(D,w_{2})}\end{equation*}

whenever

u
u

is a Lipschitz function on

D
D

,

w

1

w_{1}

is a doubling weight, and weights satisfy certain cube conditions, and

C
=
C
(
D
,
p
,
q
,

w

1

,

w

2

)

C=C(D,p,q,w_{1},w_{2})

.