共查询到20条相似文献,搜索用时 31 毫秒
1.
Let u be a weak solution of (-△)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω Rn. Then, the main goal of this paper is to prove the following a priori estimate:‖u‖ Wω2 m,p(Ω) ≤ C ‖f‖ Lωp (Ω),where ω is a weight in the Muckenhoupt class Ap. 相似文献
2.
Let u be a weak solution of (-△)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω C Rn. Then, the main goal of this paper is to prove the following a priori estimate:||u||w2m/ω·p(Ω)≤C||f||L^pω(Ω),where ω is a weight in the Muckenhoupt class Ap. 相似文献
3.
References: 《高校应用数学学报(英文版)》2007,22(1):29-36
In this note, the regularity of Poisson equation -△u = f with f lying in logarithmic function space Lp(LogL)a(Ω)(1<p <∞, a ∈ R) is studied. The result of the note generalizes the W2,p estimate of Poisson equation in Lp(Ω). 相似文献
4.
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
5.
In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf(x, u, Du)dx, (1) where Ω is an open subset of Euclidean N-space (N ≥ 3), u:Ω→ R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition |Du|p* |u|p*-a(x) ≤ f(x,u,Du) ≤ L(|Du|p+|u|p* + a(x)), (2) where L≥1, 1pN,p* = Np/N-p , and a(x) is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of (1). Our method is to compare the ω-minima of (1) with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal. 相似文献
6.
In this paper,we deal with the blow-up property of the solution to the diffusion equation u_t = △u + a(x)f(u) ∫_Ωh(u)dx,x∈Ω,t0 subject to the null Dirichlet boundary condition.We will show that under certain conditions,the solution blows up in finite time and prove that the set of all blow-up points is the whole region.Especially,in case of f(s) = s~p,h(s) = s~q,0 ≤ p≤1,p + q 1,we obtain the asymptotic behavior of the blow up solution. 相似文献
7.
Xiang Rong Zhu 《数学学报(英文版)》2017,33(5):691-704
Let Ω be a bounded domain in R~n with smooth boundary. Here we consider the following Jacobian-determinant equation det u(x)=f(x),x∈Ω;u(x)=x,x∈?Ω where f is a function on Ω with min_Ω f = δ 0 and Ωf(x)dx = |Ω|. We prove that if f ∈B_(p1)~(np)(Ω) for some p∈(n,∞), then there exists a solution u ∈ B_(p1)~(np+1)(Ω)C~1(Ω) to this equation. On the other hand, we give a simple example such that u ∈ C_0~1(R~2, R~2) while detu does not lie in B_(p1)~(2p)(R~2) for any p∞. 相似文献
8.
This paper is concerned with the following nonlinear Dirichlet problem:{-Δpu=|u|^p*-2 u λf(x,u) x∈Ω;u=0 x∈эΩ} whereΔp^u = div(|∧u|^p-2∧u) is the p-Laplacian of u,Ω is a bounded in R^n(n≥3),1<p<n, p=pn/n-p is the critical exponent for the Sobolev imbedding,λ>0 and f(x,u)satisfies some conditions. It reaches the conclusion that this problem has infinitely many solutions. Some results as p=2 or f(x,u) = |u|^q-2 u, where 1<q<p, are generalized. 相似文献
9.
《分析论及其应用》2017,(4)
Let f be an H-periodic Hlder continuous function of two real variables.The error ‖f-Nn( p; f)‖ is estimated in the uniform norm and in the Hlder norm,where p =( pk)∞k=0 is a nonincreasing sequence of positive numbers and Nn( p; f) is the nth Nrlund mean of hexagonal Fourier series of f with respect to p =( pk)∞k=0. 相似文献
10.
Shiliang ZHAO 《数学年刊B辑(英文版)》2018,39(6):1001-1016
Let M be a complete non-compact Riemannian manifold satisfying the volume doubling property and the Gaussian upper bounds. Denote by △ the Laplace-Beltrami operator and by ▽ the Riemannian gradient. In this paper, the author proves the weighted reverse inequality ‖△ 1/2 f‖Lp(ω) ≤ C‖|▽f|‖Lp(ω), for some range of p determined by M and w. Moreover, a weak type estimate is proved when p = 1. Some weighted vector-valued inequalities are also established. 相似文献
11.
After studying in a previous work the smoothness of the space UΓ0={u∈W1,p(·)(Ω);u=0 on Γ0 Γ=Ω},where dΓ-measΓ0>0,with p(·)∈C(Ω)and p(x)>1 for all x∈Ω,the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space.The results obtained in this direction are used for proving existence results for operator equations having the form Ju=Nfu,where J is a duality mapping on UΓ0 corresponding to the gauge function,and Nf is the Nemytskij operator generated by a Carath′eodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from UΓ0 into its dual. 相似文献
12.
EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE SOBOLEV-HARDY TYPE
We study the existence of solutions to the following parabolic equation{ut-△pu=λ/|x|s|u|q-2u,(x,t)∈Ω×(0,∞),u(x,0)=f(x),x∈Ω,u(x,t)=0,(x,t)∈Ω×(0,∞),(P)}where-△pu ≡-div(|▽u|p-2▽u),1
相似文献
13.
WangJianli ZhouSongping 《分析论及其应用》2003,19(3):280-288
The present paper deals with best onesided approximation rate in Lp spaces ^~En(f)Lp of f∈C2π.Although it is clear that the estimate ^~E(f)Lp≤C‖f‖Lp cannot be correct for all f∈L^p2π in case p<∞, the question whether ~En(f)Lp≤Cω(f,n^-l)Lp or ^~En(f)Lp≤CEn(f)Lp holds for f∈ C2π remains totally untouched.Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis. 相似文献
14.
Bao-huai Sheng 《应用数学学报(英文版)》2005,21(4):529-536
Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f(x)∈L^p(S^q-1),f(x)≥0,f absohutely unegual to 0,1≤p≤+∞,Then,it is proved in the present paper that there is a spherical harmonics PN(x) of order≤N and a constant C〉0 such that where ω(f,δ)L^p=sup 0〈t≤δ‖St(f)-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω(f,N^-1)L^p,St(f,μ)=1/|S^q-2|Sin^2λt ∫-μμ’=t f(μ')dμ' is a translation operator. 相似文献
15.
韩丕功 《数学物理学报(B辑英文版)》2005,25(3):533-544
This paper deals with the existence of solutions to the elliptic equation -△uμu/|x|2=λu |u|2*-2u f(x, u) in Ω, u = 0 on ( a)Ω, where Ω is a bounded domain in RN(N≥3),0∈Ω,2*=2N/N-2,λ>0,λ(a)σμ, σμ is the spectrum of the operator -△- μI/|x|2with zero Dirichlet boundary condition, 0 <μ<-μ,-μ=(N-2)2/4,f(x,u) is an asymmetric lower order perturbation of |u|2*-1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved. 相似文献
16.
LetΩRn be a bounded domain with a smooth boundary.We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term utt+αut-△u-∫0t 0μ(t-s)|u(s)| βu(s)ds + g(u)=f.Based on a time-uniform priori estimate method,the existence of the compact global attractor is proved for this model in the phase space H10(Ω)×L2(Ω). 相似文献
17.
HU Zhangjian & TANG Xiaomin Department of Mathematics Huzhou Teachers College Huzhou China 《中国科学A辑(英文版)》2006,49(8)
LetΩ Rn be a bounded convex domain with C2 boundary. For 0
相似文献
18.
This paper is concerned with the existence of positive solutions of the following Dirichlet problem for p-mean curvature operator with critical exponent: -div((1 |▽u|~2)(p-2)/2▽u)=λu~(p*-1) μu~(q-1),u>0,x∈Ω, u=0,x∈■Ω, where u∈W_0~(1,p)(Ω),Ωis a bounded domain in R~N(N>p>1)with smooth boundary ■Ω,2<=p<=q<=P~*,P~*=(Np)/(N-p),λ,P>0.It reaches the conclusions that this problem has at least one positive solution in the different cases.It is discussed the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with critical exponent by using Nehari-type duality property firstly.As p=2,q=p,the result is correspond to that of Laplace operator. 相似文献
19.
In this article,we study the initial boundary value problem of generalized Pochhammer-Chree equation u_(tt)-u_(xx)-u_(xxt)-u_(xxtt)=f(u) xx,x ∈Ω,t 0,u(x,0) = u0(x),u t(x,0)=u1(x),x ∈Ω,u(0,t) = u(1,t) = 0,t≥0,where Ω=(0,1).First,we obtain the existence of local W k,p solutions.Then,we prove that,if f(s) ∈ΩC k+1(R) is nondecreasing,f(0) = 0 and |f(u)|≤C1|u| u 0 f(s)ds+C2,u 0(x),u 1(x) ∈ΩW k,p(Ω) ∩ W 1,p 0(Ω),k ≥ 1,1 p ≤∞,then for any T 0 the problem admits a unique solution u(x,t) ∈ W 2,∞(0,T;W k,p(Ω) ∩ W 1,p 0(Ω)).Finally,the finite time blow-up of solutions and global W k,p solution of generalized IMBq equations are discussed. 相似文献
20.
HONG Jiaxing WANG Weiye 《偏微分方程(英文版)》2009,(3):234-265
In the present paper the regularity of solutions to Dirichlet problem of degenerate elliptic Monge-Ampere equations is studied. Let Ω R^2 be smooth and convex. Suppose that u ∈ C^2(^-Ω) is a solution to the following problem: det(uij) = K(x)f(x,u, Du) in Ω with u = 0 on аΩ. Then u ∈ C^∞(f)) provided that f(x,u,p) is smooth and positive in ^-Ω × R × R^2, K〉0 in Ω and near αΩ, K = d^m ^-K, where d is the distance to αΩ, m some integer bigger than 1 and ^-K smooth and positive on ^-Ω. 相似文献