共查询到20条相似文献,搜索用时 390 毫秒
1.
Piotr Kot 《Czechoslovak Mathematical Journal》2009,59(2):371-379
We solve the following Dirichlet problem on the bounded balanced domain with some additional properties: For p > 0 and a positive lower semi-continuous function u on ∂Ω with u(z) = u(λ z) for |λ| = 1, z ∈ ∂Ω we construct a holomorphic function f ∈ (Ω) such that for z ∈ ∂Ω, where = {λ ∈ ℂ: |λ| < 1}.
相似文献
2.
Rosa M. Migo-Roig 《manuscripta mathematica》1993,80(1):89-94
We show the following theorem of compensated compactness type: Ifu
n
⇁u weakly in the spaceH
1,p
(Ω, ℝ
k
) and if also
in the sense of distributions then ∂α(∣∇u∣
p-2∂α
u)=0. This result has applications in the partial regularity theory ofp-stationary mappings Ω→S
k
−1. 相似文献
3.
4.
A. Arkhipova 《Journal of Mathematical Sciences》2011,176(6):732-758
We prove the existence of a global heat flow u : Ω ×
\mathbbR+ ? \mathbbRN {\mathbb{R}^{+}} \to {\mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×
\mathbbR+ {\mathbb{R}^{+}}) ⊂
\mathbbRn {\mathbb{R}^{n}}),
n \geqslant 2 n \geqslant 2 , and
\mathbbRN {\mathbb{R}^{N}}) with boundary ∂
[`(W)] \bar{\Omega } such that φ(∂Ω) ⊂
\mathbbRN {\mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles. 相似文献
5.
Manel Sanchón 《Potential Analysis》2007,27(3):217-224
We consider the equation on a smooth bounded domain of with zero Dirichlet boundary conditions where p ≥ 2, λ > 0 and f satisfies typical assumptions in the subject of extremal solutions. We prove that, for such general nonlinearities f, the extremal solution u
* belongs to L
∞ (Ω) if N < p + p/(p − 1) and if N < p(1 + p/(p − 1)).
This work was partially supported by MCyT BMF 2002-04613-CO3-02. 相似文献
6.
Jorge García-Melián 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(4):594-607
In this paper we consider the boundary blow-up problem Δpu = a(x)uq in a smooth bounded domain Ω of , with u = +∞ on ∂Ω. Here is the well-known p-Laplacian operator with p > 1, q > p − 1, and a(x) is a nonnegative weight function which can be singular on ∂Ω. Our results include existence, uniqueness and exact boundary
behavior of positive solutions.
相似文献
7.
Rejeb HADIJI 《数学年刊B辑(英文版)》2007,28(3):327-352
The authors consider the problem: -div(p▽u) = uq-1 λu, u > 0 inΩ, u = 0 on (?)Ω, whereΩis a bounded domain in Rn, n≥3, p :Ω→R is a given positive weight such that p∈H1 (Ω)∩C(Ω),λis a real constant and q = 2n/n-2, and study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem. 相似文献
8.
Mihai Mihăilescu 《Czechoslovak Mathematical Journal》2008,58(1):155-172
We study the boundary value problem in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝ
N
. Our attention is focused on two cases when , where m(x) = max{p
1(x), p
2(x)} for any x ∈ or m(x) < q(x) < N · m(x)/(N − m(x)) for any x ∈ . In the former case we show the existence of infinitely many weak solutions for any λ > 0. In the latter we prove that if λ is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized
Lebesgue-Sobolev spaces, combined with a ℤ2-symmetric version for even functionals of the Mountain Pass Theorem and some adequate variational methods. 相似文献
9.
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
10.
Let Ω be a bounded domain with a smooth C
2 boundary in ℝn (n ≥ 3), 0 ∈
, and υ denote the unit outward normal to ∂Ω. In this paper, we are concerned with the following class of boundary value problems:
where 2* = 2n/(n − 2) is the limiting exponent for the embedding of H
1(Ω) into L
p
(Ω), 2 < p < 2*,
, η ≥ 0 and λ ∈ ℝ1 are parameters, and α(x) ∈ C(∂Ω), α(x) ≥ 0. Through a compactness analysis of the functional corresponding to the problem (*), we obtain the existence of positive
solutions for this problem under various assumptions on the parameters μ, λ and the fact that 0 ∈ Ω or 0 ∈ ∂Ω.
The research was supported by NSFC(10471052, 10571069, 10631030) and the Key Project of Chinese Ministry of Education(107081)
and NCET-07-0350. 相似文献
(*) |
11.
Juha Lehrbäck 《manuscripta mathematica》2008,127(2):249-273
We establish necessary and sufficient conditions for a domain to admit the (p, β)-Hardy inequality , where d(x) = dist(x, ∂Ω) and . Our necessary conditions show that a certain dichotomy holds, even locally, for the dimension of the complement Ω
c
when Ω admits a Hardy inequality, whereas our sufficient conditions can be applied in numerous situations where at least
a part of the boundary ∂Ω is “thin”, contrary to previously known conditions where ∂Ω or Ω
c
was always assumed to be “thick” in a uniform way. There is also a nice interplay between these different conditions that
we try to point out by giving various examples.
The author was supported in part by the Academy of Finland. 相似文献
12.
D. V. Maksimov 《Journal of Mathematical Sciences》2008,148(6):850-859
Consider functions u1, u2,..., un ∈ D(ℝk) and assume that we are given a certain set of linear combinations of the form ∑i, j a
ij
(l)
∂jui. Sufficient conditions in terms of coefficients a
ij
(l)
are indicated under which the norms
are controlled in terms of the L1-norms of these linear combinations. These conditions are mostly transparent if k = 2. The classical Gagliardo inequality
corresponds to a single function u1 = u and the collection of its partial derivatives ∂1u,..., ∂ku. Bibliography: 2 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 120–139. 相似文献
13.
In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem
of optimizing the cost functional
over some admissible class of loads f where u is the (unique) solution to the problem −Δ
p
u+|u|
p−2
u=0 in Ω with |∇
u|
p−2
u
ν
=f on ∂Ω.
Supported by Universidad de Buenos Aires under grant X078, by ANPCyT PICT No. 2006-290 and CONICET (Argentina) PIP 5478/1438.
J. Fernández Bonder is a member of CONICET. Leandro M. Del Pezzo is a fellow of CONICET. 相似文献
14.
Annunziata Loiudice 《manuscripta mathematica》2007,124(2):247-259
We prove existence and multiplicity of solutions for the semilinear subelliptic problem with critical growth in Ω, u = 0 on ∂Ω, where is a sublaplacian on a Carnot group , 2* = 2Q/(Q − 2) is the critical Sobolev exponent for and Ω is a bounded domain of . 相似文献
15.
We prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations
where u>e, W={(W
t
1,…,W
t
k
),0≤t≤1} is a standard k-dimensional Wiener process,
are functions of class
with bounded partial derivatives up to order 2, X
0
u
is a random vector not necessarily adapted and the first integral is a generalized Stratonovich integral.
The work is partially supported by DGES grant BFM2003-01345. 相似文献
16.
Kentaro Hirata 《Potential Analysis》2009,30(2):165-177
In an unbounded domain Ω in ℝ
n
(n ≥ 2) with a compact boundary or Ω = ℝ
n
, we investigate the existence of limits at infinity of positive superharmonic functions u on Ω satisfying a nonlinear inequality like as
where Δ is the Laplacian and c > 0 and p > 0 are constants. The result is applicable to positive solutions of semilinear elliptic equations of Matukuma type.
This work was partially supported by Grant-in-Aid for Young Scientists (B) (No. 19740062), Japan Society for the Promotion
of Science. 相似文献
17.
Roberta Tognari 《Potential Analysis》2007,26(2):163-188
We consider the operator in L
2(B, ν) and in L
1(B, ν) with Neumann boundary condition, where U is an unbounded function belonging to for some q ∈(1, ∞), B is the possibly unbounded convex open set in where U is finite and ν(dx) = C exp (−2U (x))dx is a probability measure, infinitesimally invariant for N
0. We prove that the closure of N
0 is a m-dissipative operator both in L
2(B, ν) and in L
1(B, ν). Moreover we study the properties of ergodicity and strong mixing of the measure ν in the L
2 case.
相似文献
18.
We study the existence of an integral representation for the functional
when μ is a positive Radon measure on ℝN, Ω⊂ℝN is a bounded open set, and
is a continuous function not necessarily convex with growth conditions of order p>1.
Mathematics Subject Classification (2000) 49J45, 49Q20 相似文献
19.
A. I. Sergeev 《Journal of Mathematical Sciences》1998,92(1):3635-3639
M. Riesz potentials
are considered, where Ω is a domain in ℝn+1 with a nice boundary ∂Ω, and μ is a Borel charge on ∂Ω. These potentials satisfy the Darboux equation
Theorems of the following kind are proved: if U
α
μ
and μ decrease rapidly in a vicinity of a point p∈ϖΩ along “normality properties,” i.e., with the properties of uniform boundedness
(on compact subsets of Ω) of potentials U
α
μ
(and solutions of (1), respectively), which satisfy some growth restrictions along ∂Ω. Bibliography: 10 titles.
Translated fromZapski Nauchnykh, Seminarov POMI, Vol. 232, 1996, pp. 141–147.
Traslated by I. A. Fedortsova. 相似文献
((1)) |
20.
Linghai ZHANG 《数学年刊B辑(英文版)》2008,29(2):179-198
Let u=u(x,t,uo)represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt+δux+γHuxx+βuxxx+f(u)x=αuxx,u(x,0)=uo(x), whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f(0)=0,|f(u)|→∞as |u|→∞,and f∈C^1(R),and there exist the following limits Lo=lim sup/u→o f(u)/u^3 and L∞=lim sup/u→∞ f(u)/u^5 Suppose that the initial function u0∈L^I(R)∩H^2(R).By using energy estimates,Fourier transform,Plancherel's identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv(xxt)+δvx+γHv(xx)+βv(xxx)=αv(xx),v(x,0)=vo(x), the author justifies the following limits(with sharp rates of decay) lim t→∞[(1+t)^(m+1/2)∫|uxm(x,t)|^2dx]=1/2π(π/2α)^(1/2)m!!/(4α)^m[∫R uo(x)dx]^2, if∫R uo(x)dx≠0, where 0!!=1,1!!=1 and m!!=1·3…(2m-3)…(2m-1).Moreover lim t→∞[(1+t)^(m+3/2)∫R|uxm(x,t)|^2dx]=1/2π(x/2α)^(1/2)(m+1)!!/(4α)^(m+1)[∫Rρo(x)dx]^2, if the initial function uo(x)=ρo′(x),for some functionρo∈C^1(R)∩L^1(R)and∫Rρo(x)dx≠0. 相似文献