共查询到20条相似文献,搜索用时 31 毫秒
1.
在变指数Lebesgue空间Lp(x)(Ω)、变指数Sobolev空间W~1,p(x)(Ω)、加权变指数Lebesgue空间Lp(x)(Ω;|x~(α(x)))和加权变指数Sobolev空间W~1,p(x)(Ω;|x|~(a(x)))的基本理论体系的基础上利用山路引理得到一类p(x)-Laplace方程非平凡解的存在性. 相似文献
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Let Ω be a domain in RN. It is shown that a generalized Poincaré inequality holds in cones contained in the Sobolev space W1,p(·)(Ω), where p(·) :(-Ω)→ [1,∞[ is a variable exponent. This inequality is itself a corollary to a more general result about equivalent norms over such cones. The approach in this paper avoids the difficulty arising from the possible lack of density of the space D(Ω) in the space {v ∈ W1,p(·)(Ω);tr v= 0 on aΩ}. Two applications are also discussed. 相似文献
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本文讨论了Ω上如下一类带临界增长的椭圆方程在拟超临界的Neumann边界条件下正解的存在性:-Div(| u |p-2 u) =λum up*-1,-| u |p-2 u ν=ψ(x)uq-1,x∈Ω,x∈Ω.这里Ω∈RN,(N≥3)是光滑有界区域, 1≤p < N,0< m < p-1,(N -1)pN - p= p*N-1 ≤q < p*,其中p* =NpN - p是W1,p(Ω)→Ls(Ω)的Sobolev临界指数,p*N-1 =(N -1)pN - p是W1,p(Ω)→Lt( Ω)的在(N-1)维流形上的临界指数,λ>0是一个正参数. 相似文献
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在广义Lebesgue空间Lp~(x)(Ω)和广义Sobolev空间W~(1,p(x))(Ω)的基本理论体系的基础上得到了一类p(x)-Laplace方程满足广义(PS)条件的一个充分条件. 相似文献
6.
《Journal of Differential Equations》2004,198(1):129-148
In this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W1,p(Ω)?Lq(∂Ω) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Ω, W1,p(P(Ω),α)?Lq(P(Ω),β).For the special case p=q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. 相似文献
7.
Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space 下载免费PDF全文
Youssef Akdim & Chakir Allalou 《数学研究》2015,48(4):375-397
In this article, we study a general class of nonlinear degenerated elliptic
problems associated with the differential inclusion $β(u)-div(a(x,Du)+F(u)) ∋ f$ in $Ω$ where $f ∈ L^1(Ω).$ A vector field $a(.,.)$ is a Carathéodory function. Using truncation
techniques and the generalized monotonicity method in the framework of weighted
variable exponent Sobolev spaces, we prove existence of renormalized solutions for
general $L^1$-data. 相似文献
8.
Norbert Weck 《Mathematical Methods in the Applied Sciences》2004,27(2):155-162
By a general argument, it is shown that Herglotz wave functions are dense (with respect to the C∞(Ω)‐topology) in the space of all solutions to the reduced wave equation in Ω. This is used to provide corresponding approximation results in global spaces (eg. in L2‐Sobolev‐spaces Hm(Ω)) and for boundary data. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
Andrea Cianchi 《Advances in Mathematics》2008,217(5):2005-2044
Sharp constants in exponential inequalities involving a general class of measures in domains Ω⊂Rn are exhibited in the limiting case of the Sobolev embedding theorem. A comprehensive approach is presented yielding, as special instances, trace inequalities on ∂Ω, on smooth submanifolds of Ω of arbitrary dimension, and also on fractal subsets of Ω, and recovering, in particular, the classical Moser-Trudinger inequality. 相似文献
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Julián Fernández Bonder Julio D. Rossi Noemi Wolanski 《Bulletin des Sciences Mathématiques》2006,130(7):565
We study the dependence on the subset A⊂Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p=2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction. 相似文献
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Pham The Lai 《Israel Journal of Mathematics》1974,17(4):364-379
We compute here the class of compacity of those operators onL 2 (Ω) the image of which belongs to some families of weighted Sobolev spaces. Such spaces are relevant for the study of some elliptic problems which degenerate at the boundary of Ω. 相似文献
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The existence of catΩ(Ω) positive solutions for the p-Laplacian system with convex and Sobolev critical nonlinearities is obtained by some standard variational methods, whose key is to construct homotopies between Ω and levels of the functional Jλ,μ, and some analytical techniques. 相似文献
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Sobolev临界增长椭圆方程注 总被引:1,自引:0,他引:1
利用空间H10(Ω)的正交分解和极小值原理给出了具临界指数2*的椭圆方程-Δu=λ1u-|u|2*-2u+g(x,u)+h(x)1解的存在性定理,这里次临界项g(x,u)关于u是非线性的,λ1为算子-Δ在H10(Ω)中最小特征值.特别当h≡0时,本文还获得了非零解的存在性结论. 相似文献
14.
(K_1,K_2)-拟正则映射的L_p可积性 总被引:6,自引:0,他引:6
对于Sobolev类W1,nloc(Ω,Rn)的n维(K1,K2)-拟正则映射,建立了其偏微商的Lp可积性结果,从而得到映射的H¨older连续性;并且给出了其对一类拟线性椭圆型方程组先验估计的应用 相似文献
15.
We study the embeddings E : W(X(Ω), Y(Ω)) ↪ Z(Ω), where X(Ω), Y(Ω) and Z(Ω) are rearrangement–invariant Banach function spaces (BFS) defined on a generalized ridged domain Ω, and W denotes a first–order Sobolev–type space. We obtain two–sided estimates for the measure of non–compactness of E when Z(Ω) = X(Ω) and, in turn, necessary and sufficient conditions for a Poincaré–type inequality to be valid and also for E to be compact. The results are used to analyse the example of a trumpet–shaped domain Ω in Lorentz spaces. We consider the problem of determining the range of possible target spaces Z(Ω), in which case we prove that the problem is equivalent to an analogue on the generalized ridge Γ of Ω. The range of target spaces Z(Ω) is determined amongst a scale of (weighted) Lebesgue spaces for “rooms and passages” and trumpet–shaped domains. 相似文献
16.
Norbert Weck 《Mathematical Methods in the Applied Sciences》2004,27(5):603-621
By a general argument, it is shown that Maxwell–Herglotz‐fields are dense (with respect to the C∞(Ω)‐topology) in the space of all solutions to Maxwell's equations in Ω. This is used to provide corresponding approximation results in global spaces (e.g. in L2‐Sobolev‐spaces Hm(Ω)) and for boundary data. Proofs are given within the framework of generalized Maxwell's equations using differential forms. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
17.
Pier Domenico Lamberti 《Journal of Differential Equations》2005,216(1):109-133
Let Ω be an open connected subset of Rn of finite measure for which the Poincaré-Wirtinger inequality holds. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset φ(Ω) of Rn, where φ is a locally Lipschitz continuous homeomorphism of Ω onto φ(Ω). Then, we show Lipschitz-type inequalities for the reciprocals of the eigenvalues delivered by the Rayleigh quotient. Then, we further assume that the imbedding of the Sobolev space W1,2(Ω) into the space L2(Ω) is compact, and we prove the same type of inequalities for the projections onto the eigenspaces upon variation of φ. 相似文献
18.
We consider in this paper a system of equations modelling a steady-state induction heating process for ‘two-dimensional geometries’. Existence of a solution is stated in W1,p(Ω) Sobolev spaces and is derived using the Leray–Schauder's fixed point theory. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
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N. Baranibalan K. Sakthivel J.-H. Kim 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(6):2841-2851
In this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain Ω⊂Rn for the dimension n≤3 with a single observation on a subdomain ω?Ω and the Sobolev norm of certain partial derivatives of the solutions at a fixed positive time θ∈(0,T) over the whole spatial domain. The proof of these results relies on an appropriate Carleman estimate for the phase field system. 相似文献