共查询到20条相似文献,搜索用时 15 毫秒
1.
Omar Anza Hafsa Jean-Philippe Mandallena 《Annali di Matematica Pura ed Applicata》2007,186(1):185-196
Consider a plate occupying in a reference configuration a bounded open set Ω ⊂ ℝ
2
, and let
be its stored-energy function. In this paper we are concerned with relaxation of variational problems of type:
, where
with
is the scalar product in ℝ
3
and
is the external loading per unit surface. We take into account the fact that an infinite amount of energy is required to compress
a finite surface of the plate into zero surface, i.e.,
Mathematics Subject Classification (2000) 49J45 相似文献
2.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
3.
Adimurthi K. Sandeep 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):585-603
Let Ω be a bounded domain in
, we prove the singular Moser-Trudinger embedding:
if and only if
where
and
. We will also study the corresponding critical exponent problem. 相似文献
4.
Giovanna Cerami 《Milan Journal of Mathematics》2006,74(1):47-77
In this paper the results of some investigations concerning nonlinear elliptic problems in unbounded domains are summarized
and the main difficulties and ideas related to these researches are described.
The model problem
where
, N ≥ 3, is an unbounded smooth domain, a(x) is a smooth real function defined on Ω, such that
, is considered and existence and multiplicity results are given under various assumptions on Ω.
Work supported by national research project “Metodi variazionali e topologici nello studio di fenomeni non lineari".
Lecture held in the Seminario Matematico e Fisico on February 28, 2005
Received: June 2006 相似文献
5.
Abdelmajid Siai 《Potential Analysis》2006,24(1):15-45
Let Ω be an open bounded set in ℝN, N≥3, with connected Lipschitz boundary ∂Ω and let a(x,ξ) be an operator of Leray–Lions type (a(⋅,∇u) is of the same type as the operator |∇u|p−2∇u, 1<p<N). If τ is the trace operator on ∂Ω, [φ] the jump across ∂Ω of a function φ defined on both sides of ∂Ω, the normal derivative
∂/∂νa related to the operator a is defined in some sense as 〈a(⋅,∇u),ν〉, the inner product in ℝN, of the trace of a(⋅,∇u) on ∂Ω with the outward normal vector field ν on ∂Ω. If β and γ are two nondecreasing continuous real functions everywhere
defined in ℝ, with β(0)=γ(0)=0, f∈L1(ℝN), g∈L1(∂Ω), we prove the existence and the uniqueness of an entropy solution u for the following problem,
in the sense that, if Tk(r)=max {−k,min (r,k)}, k>0, r∈ℝ, ∇u is the gradient by means of truncation (∇u=DTku on the set {|u|<k}) and
, u measurable; DTk(u)∈Lp(ℝN), k>0}, then
and u satisfies,
for every k>0 and every
.
Mathematics Subject Classifications (2000) 35J65, 35J70, 47J05. 相似文献
6.
We extend the results for 2-D Boussinesq equations from ℝ2 to a bounded domain Ω. First, as for the existence of weak solutions, we transform Boussinesq equations to a nonlinear evolution
equation U
t
+ A(t, U) = 0. In stead of using the methods of fundamental solutions in the case of entire ℝ2, we study the qualities of F(u, υ) = (u · ▽)υ to get some useful estimates for A(t, U), which helps us to conclude the local-in-time existence and uniqueness of solutions. Second, as for blow-up criterions,
we use energy methods, Sobolev inequalities and Gronwall inequality to control
and
by
and
. Furthermore,
can control
by using vorticity transportation equations. At last,
can control
. Thus, we can find a blow-up criterion in the form of
.
相似文献
7.
Francesco Petitta 《Annali di Matematica Pura ed Applicata》2008,187(4):563-604
Let a bounded open set, N ≥ 2, and let p > 1; we prove existence of a renormalized solution for parabolic problems whose model is
where T > 0 is a positive constant, is a measure with bounded variation over , and is the usual p-Laplacian.
相似文献
8.
An analog of the classical Fourier formula for the characteristic function of a convex compact set
is considered:
where W is a polyhedral in
. Bibliography: 6 titles. 相似文献
9.
We prove that if f belongs to the Morrey space
, with λ ∊ [0, n−2], and u is the solution of the problem
then Du belongs to the space
, for any
Mathematics Subject Classification (2000) 35J25, 35D10 相似文献
10.
Given a Lévy process \(\xi \), we find necessary and sufficient conditions for almost sure finiteness of the perpetual integral \(\int _0^\infty f(\xi _s)\hbox {d}s\), where \(f\) is a positive locally integrable function. If \(\mu =\mathbb {E}[\xi _1]\in (0,\infty )\) and \(\xi \) has local times we prove the 0–1 law with the exact characterization The proof uses spatially stationary Lévy processes, local time calculations, Jeulin’s lemma and the Hewitt–Savage 0–1 law.
相似文献
$$\begin{aligned} \mathbb {P}\Big (\int _0^\infty f(\xi _s)\,\hbox {d}s<\infty \Big )\in \{0,1\} \end{aligned}$$
$$\begin{aligned} \mathbb {P}\Big (\int _0^\infty f(\xi _s)\,\hbox {d}s<\infty \Big )=0\qquad \Longleftrightarrow \qquad \int ^\infty f(x)\,\hbox {d}x=\infty . \end{aligned}$$
11.
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
depends continuously on (a
ij
,β,γ,q).
Dedicated to Karl H. Hofmann on his 75th birthday. 相似文献
12.
Yasushi Nagata 《Annals of the Institute of Statistical Mathematics》1983,35(1):193-199
Summary LetX be a random variable from the one-parameter exponential family with the probability element β(θ) exp (θx)dm(x) for which an ambiguous prior information is available to the effect that θ is likely to be larger than or equal to a known
constant. The information is represented by a fuzzy set with the membership function χ(θ). Then it is shown that
is an admissible estimator for E
0
(X) under the quadratic loss function. 相似文献
13.
The aim of this paper is to study the well-posedness of the initial-boundary value problem
where
is a bounded regular open domain in
is the outward normal to
and
, where
are pairwise disjoint measurable subsets of
with respect to Lebesgue surface measure on
. The main novelty lies on the reactive dynamical boundary condition imposed on
. The technique makes it possible to study the more general initial-boundary value problem
where
is as before and
. A key step in our analysis consists in studying the eigenvalue problem
相似文献
14.
G. A. Afrouzi Nguyen Thanh Chung Z. Naghizadeh 《Mediterranean Journal of Mathematics》2014,11(3):891-903
Using variational methods, we study the existence and nonexistence of nontrivial weak solutions for the quasilinear elliptic system $$\left\{\begin{array}{ll}- {\rm div}(h_1(|\nabla u|^2)\nabla u) = \frac{\mu}{|x|^2}u + \lambda F_u(x, u, \upsilon)\quad {\rm in}\,\Omega,\\- {\rm div}(h_2(|\nabla \upsilon|^2)\nabla \upsilon) = \frac{\mu}{|x|^2}\upsilon + \lambda F_\upsilon(x,u,\upsilon)\quad {\rm in}\,\Omega,\\u = \upsilon = 0 \qquad \qquad \qquad \qquad \qquad \qquad {\rm in}\, \partial\Omega, \end{array}\right.$$ where \({\Omega \subset \mathbb{R}^N,N \geq 3}\) , is a bounded domain containing the origin with smooth boundary \({\partial \Omega ; h_i, i = 1, 2}\) , are nonhomogeneous potentials; \({(F_u, F_v) = \nabla F}\) stands for the gradient of a sign-changing C 1-function \({F : \Omega \times \mathbb{R}^2 \to \mathbb{R}}\) in the variable \({{w = (u, v) \in \mathbb{R}^2}}\) ; and λ and μ are parameters. 相似文献
15.
Nguyen Thanh Chung 《Acta Appl Math》2010,110(1):47-56
This paper deals with the existence of weak solutions to a class of degenerate and singular elliptic systems in ℝ
N
, N
≧2 of the form
$\left\{{l@{\quad}l}-\mathop{\mathrm{div}}(h_{1}(x)\nabla u)+a(x)u=f(x,u,v)&\mbox{in}\mathbb{R}^{N},\\-\mathop{\mathrm{div}}(h_{2}(x)\nabla v)+b(x)v=g(x,u,v)&\mbox{in}\mathbb{R}^{N},\right.$\left\{\begin{array}{l@{\quad}l}-\mathop{\mathrm{div}}(h_{1}(x)\nabla u)+a(x)u=f(x,u,v)&\mbox{in}\mathbb{R}^{N},\\-\mathop{\mathrm{div}}(h_{2}(x)\nabla v)+b(x)v=g(x,u,v)&\mbox{in}\mathbb{R}^{N},\end{array}\right. 相似文献
16.
G. Bouchitte 《Annali dell'Universita di Ferrara》1987,33(1):113-156
Résumé Partant d’un résultat abstrait de représentation intègrale pour une fonctionnelle convexe faiblement s.c.i. sur [M
b
(Ω)]
d
(obtenu grace à [1]); on établit un résultat de convergence pour une suite de fonctionnelles du type
μ
n
εM
b
+
(Ω),f
n
: Ω×R
d
→−∞, +∞] inté
Quelques exemples motivés par des applications à la mécanique sont ensuite traités.
Riassunto Partendo da un risultato astratto di rappresentazione integrale per un funzionale convesso debolmente s.c.i. su [M b (Ω)] d (ottenuto grazie a [1]), si dimostra un risultato di convergenza per una successione di funzionali del tipo con μ n εM b + (Ω),f n : Ω×R d →−∞, +∞] integrando normale convesso. Vengono inoltre trattati alcuni esempi motivati da applicazioni alla Meccanica.相似文献 17.
We establish a new 3G-Theorem for the Green’s function for the half space
We exploit this result to introduce a new class of potentials
that we characterize by means of the Gauss semigroup on
. Next, we define a subclass
of
and we study it. In particular, we prove that
properly contains the classical Kato class
. Finally, we study the existence of positive continuous solutions in
of the following nonlinear elliptic problem
18.
Let X be a rearrangement-invariant Banach function space
over a complete probability space
, and denote by
the Hardy space consisting of all martingales
such that
. We prove that
implies
for any filtration
if and only if Doobs inequality holds in
X, where
denotes the martingale defined by
, n = 0, 1, 2, ..., and
a.s.Received: 1 August 2000 相似文献
19.
J. A. López Molina M. E. Puerta M. J. Rivera 《Bulletin of the Brazilian Mathematical Society》2006,37(2):191-216
Let
, be a family of compatible couples of Lp-spaces. We show that, given a countably incomplete ultrafilter
in
, the ultraproduct
of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type
, an intermediate K?the space between
and
being a purely atomic measure space, and a K?the function space K(Ω3) defined on some purely non atomic measure space (Ω3, ν3) in such a way that Ω2 ∪ Ω3 ≠∅.
The research of first and third authors is partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group
03/050. 相似文献
20.
Zhi Wen DUAN Kwang Ik KIM 《数学学报(英文版)》2007,23(6):1083-1094
This paper is concerned with a nonlocal hyperbolic system as follows utt = △u + (∫Ωvdx )^p for x∈R^N,t〉0 ,utt = △u + (∫Ωvdx )^q for x∈R^N,t〉0 ,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N, where 1≤ N ≤3, p ≥1, q ≥ 1 and pq 〉 1. Here the initial values are compactly supported and Ω belong to R^N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed. 相似文献
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