共查询到20条相似文献,搜索用时 109 毫秒
1.
本文运用旋转方法算出了n维Hardy算子H在径向—角向混合空间上的最佳界.进一步,当0<ββ从L|x|p Lθp(Rn)到L|x|qLθq(Rn)上的最佳界.通过对偶建立了共轭算子H*和Hβ*的相应结果.此外,还考虑了算子H的最佳弱型估计. 相似文献
2.
3.
4.
本文研究如下带有临界增长的分数阶Kirchhoff方程ε2s(ε2s-3∫∫R3×R3|u(x)-u(y)/|2|x-y|3+2s),x∈R3,其中M是一个连续正的Kirchhoff函数,λ>0是一个参数,3/40充分小和λ足够大时,我们首先证明了上述问题正基态解的存在性.其次,证明了基态解集中在一个由位势函数所刻画的特定集合中.最后,研究了基态解的衰减估计. 相似文献
5.
6.
该文考虑次临界Choquard方程■(0.1)多解的存在性,其中N> 3,λ是正实参数,pε=2μ*-ε,ε> 0,0 <μμ*=(2N-μ)/(N-2)是Hardy-Littlewood-Sobolev不等式意义下的临界指数.假定Ω:=int V-1(0)是RN中非空带光滑边界的有界区域,利用Lusternik-Schnirelman定理,该文证明了当λ足够大及ε充分小时,方程(0.1)至少有catΩ(Ω)个正解. 相似文献
7.
设n是大于1的整数,且n=Π_(i=1)tp_itp_i(a_i),令τ_k(a_i),令τ_k((e))(n)=Π_(p_i((e))(n)=Π_(p_i(a_i)||n)d_i(a_i).本文研究了和式D(■)=Σ_(n≤x)d(■)的渐近公式,这里d(■)=∑_(n=ab_1(a_i)||n)d_i(a_i).本文研究了和式D(■)=Σ_(n≤x)d(■)的渐近公式,这里d(■)=∑_(n=ab_12…b_i2…b_i2)1.然后基于以上结论得到了指数除数函数τ_i2)1.然后基于以上结论得到了指数除数函数τ_i((e))(n)的均值的渐近公式,并改进了前人的结果. 相似文献
8.
9.
10.
本文研究了一类与对数函数相关的n维Q型空间——Qlog,λm(Rn).首先给出Qlog,λm(Rn)的定义和一些基本性质.进而利用Poisson积分和调和函数空间Hlog,λm(R+n+1),得到了Qlog,λm(Rn)的调和延拓,以及Hlog,λm(R+n+1)的边值问题. 相似文献
11.
In 1988 Adams obtained sharp Moser–Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams' results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels satisfy suitable and explicit growth conditions, given in terms of their distribution functions; natural conditions for sharpness are also given. Most of the known results about Moser–Trudinger inequalities can be easily adapted to our unified scheme. We give some new applications of our theorems, including: sharp higher order Moser–Trudinger trace inequalities, sharp Adams/Moser–Trudinger inequalities for general elliptic differential operators (scalar and vector-valued), for sums of weighted potentials, and for operators in the CR setting. 相似文献
12.
Giuseppe Mingione 《Mathematische Annalen》2010,346(3):571-627
We show sharp local a priori estimates and regularity results for possibly degenerate non-linear elliptic problems, with data
not lying in the natural dual space. We provide a precise non-linear potential theoretic analog of classical potential theory
results due to Adams (Duke Math J 42:765–778, 1975) and Adams and Lewis (Studia Math 74:169–182, 1982), concerning Morrey
spaces imbedding/regularity properties. For this we introduce a technique allowing for a “non-local representation” of solutions
via Riesz potentials, in turn yielding optimal local estimates simultaneously in both rearrangement and non-rearrangement
invariant function spaces. In fact we also derive sharp estimates in Lorentz spaces, covering borderline cases which remained
open for some while. 相似文献
13.
Shutao Zhang & Yazhou Han 《分析论及其应用》2022,38(2):178-203
For conformal Hardy-Littlewood-Sobolev(HLS) inequalities [22] and reversed conformal HLS inequalities [8] on $\mathbb{S}^n,$ a new proof is given for the attainability
of their sharp constants. Classical methods used in [22] and [8] depends on rearrangement inequalities. Here, we use the subcritical approach to construct the extremal
sequence and circumvent the blow-up phenomenon by renormalization method. The
merit of the method is that it does not rely on rearrangement inequalities. 相似文献
14.
We show that if the complement of a Donaldson hypersurface in a closed, integral symplectic manifold has the homology of a subcritical Stein manifold, then the hypersurface is of degree one. In particular, this demonstrates a conjecture by Biran and Cieliebak on subcritical polarisations of symplectic manifolds. Our proof is based on a simple homological argument using ideas of Kulkarni–Wood.
相似文献15.
We study a class of traffic flow models with nonlocal look-ahead interactions. The global regularity of solutions depend on the initial data. We obtain sharp critical threshold conditions that distinguish the initial data into a trichotomy: subcritical initial conditions lead to global smooth solutions, while two types of supercritical initial conditions lead to two kinds of finite time shock formations. The existence of non-trivial subcritical initial data indicates that the nonlocal look-ahead interactions can help avoid shock formations, and hence prevent the creation of traffic jams. 相似文献
16.
We present a variational approach to study the energy-critical Schrödinger equations with subcritical perturbations. Through analysing the Hamiltonian property we establish two types of invariant evolution flows, and derive a new sharp energy criterion for blowup of solutions for the equation. Furthermore, we answer the question: how small are the initial data such that the solutions of this equation are bounded in H 1(R N )? 相似文献
17.
Nguyen Lam 《Potential Analysis》2017,46(1):75-103
In this paper, we study on \(\mathbb {R}^{2}\) some new types of the sharp subcritical and critical Trudinger-Moser inequality that have close connections to the study of the optimizers for the classical Trudinger-Moser inequalities. For instance, one of our results can be read as follows: Let 0 ≤ β < 2, p ≥ 0, α ≥ 0. Thenif and only if α < 4π or α = 4π, p ≥ 2. The attainability and inattainability of these sharp inequalties will be also investigated using a new approach, namely the relations between the supremums of the sharp subcritical and critical ones. This new method will enable us to compute explicitly the supremums of the subcritical Trudinger-Moser inequalities in some special cases. Also, a version of Concentration-compactness principle in the spirit of Lions ( Lions, I. Rev. Mat. Iberoam. 1(1) 145–01 1985) will also be studied.
相似文献
$$\sup_{\left\Vert \nabla u\right\Vert_{2}^{2}+\left\Vert u\right\Vert_{2} ^{2}\leq1}\left\Vert u\right\Vert_{2}^{p}{\int}_{\mathbb{R}^{2}}\exp\left( \alpha\left( 1-\frac{\beta}{2}\right) \left\vert u\right\vert^{2}\right) \left\vert u\right\vert^{2}\frac{dx}{\left\vert x\right\vert^{\beta}}<\infty $$
18.
Alessandro Palmieri 《Mathematical Methods in the Applied Sciences》2020,43(11):6702-6731
In this note, two blow-up results are proved for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms both in the subcritical case and in the critical case when the damping and the mass terms make both equations in some sense “wave-like.” In the proof of the subcritical case, an iteration argument is used. This approach is based on a coupled system of nonlinear ordinary integral inequalities and lower bound estimates for the spatial integral of the nonlinearities. In the critical case, we employ a test function-type method that has been developed recently by Ikeda-Sobajima-Wakasa and relies strongly on a family of certain self-similar solutions of the adjoint linear equation. Therefore, as critical curve in the p−q plane of the exponents of the power nonlinearities for this weakly coupled system, we conjecture a shift of the critical curve for the corresponding weakly coupled system of semilinear wave equations. 相似文献
19.
Cristina Tarsi 《Potential Analysis》2012,37(4):353-385
We exhibit sharp embedding constants for Sobolev spaces of any order into Zygmund spaces, obtained as the product of sharp embedding constants for second order Sobolev space into Lorentz spaces. As a consequence, we derive a new proof of Adams?? inequality, which holds in the larger hypotheses of homogenoeous Navier boundary contidions. 相似文献
20.
Yue HE 《Frontiers of Mathematics in China》2015,10(6):1283
We give an easy proof of Andrews and Clutterbuck’s main results [J. Amer. Math. Soc., 2011, 24(3): 899−916], which gives both a sharp lower bound for the spectral gap of a Schrödinger operator and a sharp modulus of concavity for the logarithm of the corresponding first eigenfunction. We arrive directly at the same estimates by the ‘double coordinate’ approach and asymptotic behavior of parabolic flows. Although using the techniques appeared in the above paper, we partly simplify the method and argument. This maybe help to provide an easy way for estimating spectral gap. Besides, we also get a new lower bound of spectral gap for a class of Schödinger operator. 相似文献