共查询到20条相似文献,搜索用时 609 毫秒
1.
V. A. Kondratiev 《Journal of Mathematical Sciences》2006,135(1):2666-2674
The equations under consideration have the following structure:
where 0 < x
n < ∞, (x
1, …, x
n−1) ∈ Ω, Ω is a bounded Lipschitz domain,
is a function that is continuous and monotonic with respect to u, and all coefficients are bounded measurable functions. Asymptotic formulas are established for solutions of such equations
as x
n → + ∞; the solutions are assumed to satisfy zero Dirichlet or Neumann boundary conditions on ∂Ω. Previously, such formulas
were obtained in the case of a
ij, ai depending only on (x
1, …, x
n−1).
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 98–111, 2005. 相似文献
2.
Let Ω⊂R
n
(n≥2) be a bounded open set;Q
T
=Ω×[0,T],S
T
=δΩ×[0,T],S
1,S
2 be the partial boundaries of Ω andS
1∪S
2=δΩ,S
1∩S
2=Φ. We denote Γ1.T
=S
1×[0,T], Γ2.T
=S
2×[0,T], and consider the problem
相似文献
3.
Giuseppe Maria Coclite Angelo Favini Gisèle Ruiz Goldstein Jerome A. Goldstein Silvia Romanelli 《Semigroup Forum》2008,77(1):101-108
The solution u of the well-posed problem
4.
P. Z. Mkrtychyan 《Journal of Mathematical Sciences》1985,28(5):742-750
In a bounded domain of the n -dimensional (n?2) space one considers a class of degenerate quasilinear elliptic equations, whose model is the equation $$\sum\limits_{i = 1}^n {\frac{{\partial F}}{{\partial x_i }}} (a^{\ell _i } (u)\left| {u_{x_i } } \right|^{m_i - 2} u_{x_i } ) = f(x),$$ where x =(x1,..., xr), li?0, mi>1, the function f is summable with some power, the nonnegative continuous function a(u) vanishes at a finite number of points and satisfies \(\frac{{lim}}{{\left| u \right| \to \infty }}a(u) > 0\) . One proves the existence of bounded generalized solutions with a finite integral $$\int\limits_\Omega {\sum\limits_{i = 1}^n {a^{\ell _i } (u)\left| {u_{x_i } } \right|^{m_i } dx} }$$ of the Dirichlet problem with zero boundary conditions. 相似文献
5.
For a singular perturbation
, n ≤ ∞, of a positive self-adjoint operator A
0 with Lebesgue spectrum, the spectral analysis of the corresponding self-adjoint operator realizations A
T
is carried out and the scattering matrix
is calculated in terms of parameters t
ij
under some additional restrictions on singular elements ψ
j
. The results obtained enable one to apply the Lax-Phillips approach in scattering theory.
__________
Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 679–688, May, 2005. 相似文献
6.
Michel Talagrand 《Israel Journal of Mathematics》1999,111(1):275-284
Consider the discrete cube Ω={0,1}
N
, provided with the uniform probabilityP. We denote byd(x, A) the Hamming distance of a pointx of Ω and a subsetA of Ω. We define the influenceI(A) of theith coordinate onA as follows. Forx in Ω, consider the pointT
i
(x) obtained by changing the value of theith coordinate. Then
We prove that we always have
Since it is easy to see that
, this recovers the well known fact that ∫Ω
d(x, A)dP(x) is at most of order
whenP(A)≥1/2. The new information is that ∫Ω
d(x, A)dP(x) can be of order
only ifA reassembles the Hamming ball {x; ∑1≤N
x
i
≥N/2}. 相似文献
7.
Alessandra Pagano 《Annali dell'Universita di Ferrara》1993,39(1):1-17
We consider a (possibly) vector-valued function u: Ω→R
N, Ω⊂R
n, minimizing the integral
, whereD
iu=∂u/∂x
i, or some more general functional retaining the same behaviour; we prove higher integrability forDu:D
1u,…,Dn−1u∈Lq, under suitable assumptions ona
i(x).
Sunto Consideriamo una funzione u: Ω→R N, Ω⊂R n che minimizzi l'integrale , doveD iu=∂u/∂xi, o un funzionale con un comportamento simile; sotto opportune ipotesi sua i(x), dimostriamo la seguente maggiore integrabilità perDu:D 1u,…,Dn−1uεLq.相似文献 8.
Dong Sheng Kang 《数学学报(英文版)》2009,25(3):435-444
Suppose Ω belong to R^N(N≥3) is a smooth bounded domain,ξi∈Ω,0〈ai〈√μ,μ:=((N-1)/2)^2,0≤μi〈(√μ-ai)^2,ai〈bi〈ai+1 and pi:=2N/N-2(1+ai-bi)are the weighted critical Hardy-Sobolev exponents, i = 1, 2,..., k, k ≥ 2. We deal with the conditions that ensure the existence of positive solutions to the multi-singular and multi-critical elliptic problem ∑i=1^k(-div(|x-ξi|^-2ai△↓u)-μiu/|x-ξi|^2(1+ai)-u^pi-1/|x-ξi|^bipi)=0with Dirichlet boundary condition, which involves the weighted Hardy inequality and the weighted Hardy-Sobolev inequality. The results depend crucially on the parameters ai, bi and #i, i -- 1, 2,..., k. 相似文献
9.
W. H. Yu 《Journal of Optimization Theory and Applications》1996,88(3):725-742
We consider the problems of dientifying the parametersa ij (x), b i (x), c(x) in a 2nd order, linear, uniformly elliptic equation, $$\begin{gathered} - \partial _i (a_{ij} (x)\partial _j u) + b_i (x)\partial _i u + c(x)u = f(x),in\Omega , \hfill \\ \partial _v u|_{\partial \Omega } = \phi (s),s \in \partial \Omega , \hfill \\ \end{gathered} $$ on the basis of measurement data $$u(s) = z(s),s \in B \subset \partial \Omega ,$$ with an equality constraint and inequality constraints on the parameters. The cost functionals are one-sided Gâteaux differentiable with respect to the state variables and the parameters. Using the Duboviskii-Milyutin lemma, we get maximum principles for the identification problems, which are necessary conditions for the existence of optimal parameters. 相似文献
10.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引:7,自引:0,他引:7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
11.
姚奎 《高校应用数学学报(英文版)》2001,16(2):161-170
§ 1 PreliminariesWe considerψ( x)∈ L1 ( Rn) satisfying the mean valuezero,i.e.∫Rnψdx=0 ,and definethe square function g( f) on Rnbyg( f) ( x) =( k|ψk* f|2 ) 1 2 ( x)for f∈ S( Rn) ,the Schwartz space,whereψk( x) =ψ2 k( x) . Whenψ has some smooth property,one can obtain the weak type estimate by viewingthe square function g( f) as the vector-valued singularintegrals,which the readercan referto [1 ,2 ] .As for the results aboutthe Lp-estimates,see [3,4 ] .In this paper,we sha… 相似文献
12.
The paper is devoted to the study of the behavior of the following mixed problem for large values of time:
13.
In this work the authors study the conditions for the existence of diffusion equations
14.
E. M. E. Zayed 《数学学报(英文版)》2000,16(4):627-636
Abstract
Small-time asymptotics of the trace of the heat semigroup
where {μ
ν
} are the eigenvalues of the negative Laplacian
in the (x
1, x
2)-plane, is studied for a general bunded domain Ω with a smooth boundary ∂Ω, where a finite number of Dirichlet, Neumann and
Robin boundary conditions, on the piecewise smooth parts Γ
i
(i = 1, ..., n) of ∂Ω such that
, are considered. Some geometrical properties associated with Ω are determined. 相似文献
15.
For x = (x 1, x 2, ..., x n ) ∈ ℝ+ n , the symmetric function ψ n (x, r) is defined by $\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } ,$\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } , 相似文献
16.
Let X
1, X
2, ... be i.i.d. random variables. The sample range is R
n
= max {X
i
, 1 ≤ i ≤ n} − min {X
i
, 1 ≤ i ≤ n}. If for a non-degenerate distribution G and some sequences (α
k
), (β
k
) then we have
17.
Teresa D'Aprile Juncheng Wei 《Calculus of Variations and Partial Differential Equations》2006,25(1):105-137
We study the following system of Maxwell-Schrödinger equations $ \Delta u - u - \delta u \psi+ f(u)=0, \quad \Delta \psi + u^2 = 0 \mbox{in} {\mathbb R}^N , u, \;\psi > 0, \quad u, \;\psi \to 0 \ \mbox{as} \ |x| \to + \infty, $ where δ > 0, u, ψ : $\psi: {\mathbb R}^N \to {\mathbb R}
18.
We consider the second order differential equation
, where (x,t)
N+1, 0<m
0N, the coefficients a
i,j
belong to a suitable space of vanishing mean oscillation functions VMO
L
and B=(b
i,j
) is a constant real matrix. The aim of this paper is to study interior regularity for weak solutions to the above equation assuming that F
j
belong to a function space of Morrey type. 相似文献
19.
Matteo Dalla Riva Massimo Lanza de Cristoforis 《Complex Analysis and Operator Theory》2011,5(3):811-833
Let Ω
i
and Ω
o
be two bounded open subsets of
\mathbbRn{{\mathbb{R}}^{n}} containing 0. Let G
i
be a (nonlinear) map from
?Wi×\mathbbRn{\partial\Omega^{i}\times {\mathbb{R}}^{n}} to
\mathbbRn{{\mathbb{R}}^{n}} . Let a
o
be a map from ∂Ω
o
to the set
Mn(\mathbbR){M_{n}({\mathbb{R}})} of n × n matrices with real entries. Let g be a function from ∂Ω
o
to
\mathbbRn{{\mathbb{R}}^{n}} . Let γ be a positive valued function defined on a right neighborhood of 0 in the real line. Let T be a map from
]1-(2/n),+¥[×Mn(\mathbbR){]1-(2/n),+\infty[\times M_{n}({\mathbb{R}})} to
Mn(\mathbbR){M_{n}({\mathbb{R}})} . Then we consider the problem
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