共查询到20条相似文献,搜索用时 46 毫秒
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Pierangelo Marcati 《Journal of Differential Equations》2003,191(2):445-469
We first obtain the Lp-Lq estimates of solutions to the Cauchy problem for one-dimensional damped wave equation
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Bernard K. Bonzi 《Journal of Mathematical Analysis and Applications》2010,370(2):392-405
We study the boundary value problem in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in RN (N?3) and is a p(x)-Laplace type operator with p(.):Ω→[1,+∞) a measurable function and b a continuous and nondecreasing function from R→R. We prove the existence and uniqueness of an entropy solution for L1-data f. 相似文献
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Let 1<p?2 and q be such that . It is well known that the norm of the Lp-Fourier transform of the additive group is , where . For a nilpotent Lie group G, we obtain the estimate , where m is the maximal dimension of the coadjoint orbits. Such a result was known only for some particular cases. 相似文献
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The L resolvents of second-order elliptic operators of divergence form under the Dirichlet condition
Yoichi Miyazaki 《Journal of Differential Equations》2004,206(2):353-372
Let A be the 2mth-order elliptic operator of divergence form with bounded measurable coefficients defined in a domain Ω of . For 1<p<∞ we regard A as a bounded linear operator from the Lp Sobolev space to H−m,p(Ω). It is known that when , we can construct the resolvent (A−λ)−1 and estimate its operator norm for some λ if the leading coefficients are uniformly continuous. In this paper, we try to extend this result to a general domain. It is successful when m=1 if Ω is the half-space or a domain with C2 bounded boundary. For m>1 it is shown that the problem is reduced to the case where Ω is the half-space and A is a homogeneous operator with constant coefficients. We also give a perturbation theorem. 相似文献
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H. Movahedi-Lankarani R. Wells 《Journal of Mathematical Analysis and Applications》2003,285(1):299-320
The C1-Weierstrass approximation theorem is proved for any compact subset X of a Hilbert space . The same theorem is also proved for Whitney 1-jets on X when X satisfies the following further condition: There exist finite dimensional linear subspaces such that ?n?1Hn is dense in and πn(X)=X∩Hn for each n?1. Here, is the orthogonal projection. It is also shown that when X is compact convex with and satisfies the above condition, then C1(X) is complete if and only if the C1-Whitney extension theorem holds for X. Finally, for compact subsets of , an extension of the C1-Weierstrass approximation theorem is proved for C1 maps with compact derivatives. 相似文献
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In this paper, we consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in nonsmooth bounded domain Ω with nonhomogeneous boundary condition u=φ on ∂Ω. Assuming , which is translation compact and φ∈L∞(∂Ω), we establish the existence of the uniform attractor in L2(Ω) and . 相似文献
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Kazuo Kobayasi 《Journal of Differential Equations》2003,189(2):383-395
We prove the equivalence of weak solutions and entropy solutions of an elliptic-parabolic-hyperbolic degenerate equation with homogeneous Dirichlet conditions and initial conditions. As a result of the equivalence, we obtain the L1-contraction principle and uniqueness of weak solutions of elliptic-parabolic degenerate equations. 相似文献
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Hideyuki Miura 《Journal of Functional Analysis》2005,218(1):110-129
We investigate a limiting uniqueness criterion to the Navier-Stokes equations. We prove that the mild solution is unique under the class , where bmo-1 is the “critical” space including Ln. As an application of uniqueness theorem, we also consider the local well-posedness of Navier-Stokes equations in bmo-1. 相似文献
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Dong Joo Moon Seoung Dal Jung 《Journal of Mathematical Analysis and Applications》2008,342(1):354-360
Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that at all x∈M and at some point x0∈M, where μ0>0 is the least eigenvalue of the Laplacian acting on L2-functions on M. Let 2?q?p. Then any q-harmonic map of finite q-energy is constant. Moreover, if N is a Riemannian manifold of non-positive scalar curvature, then any q-harmonic morphism of finite q-energy is constant. 相似文献
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Karen Yagdjian 《Journal of Differential Equations》2004,206(1):227-252
Barros-Neto and Gelfand (Duke Math. J. 98 (3) (1999) 465; Duke Math. J. 117 (2) (2003) 561) constructed for the Tricomi operator on the plane the fundamental solutions with the supports in the regions related to the geometry of the characteristics of the Tricomi operator. We give for the Tricomi-type operator a fundamental solution relative to an arbitrary point of Rn+1 with the support in the region t?0, where the operator is hyperbolic. Our key observation is that the fundamental solution for the Tricomi-type operator can be written like an integral of the distributions generated by the fundamental solution of the Cauchy problem for the wave equation. The application of that fundamental solution to the Lp-Lq estimate for the forced Tricomi-type equation is given as well. 相似文献
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Feng Dai 《Journal of Mathematical Analysis and Applications》2006,315(2):711-724
We study the Kolmogorov m-widths and the linear m-widths of the weighted Besov classes on [−1,1], where Lq,μ, 1?q?∞, denotes the Lq space on [−1,1] with respect to the measure , μ>0. Optimal asymptotic orders of and as m→∞ are obtained for all 1?p,τ?∞. It turns out that in many cases, the orders of are significantly smaller than the corresponding orders of the best m-term approximation by ultraspherical polynomials, which is somewhat surprising. 相似文献
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Mauro Spera 《Journal of Functional Analysis》2003,197(1):110-139
In this paper, a rigorous construction of the S1-equivariant Dirac operator (i.e., Dirac-Ramond operator) on the space of (mean zero) loops in is given and its equivariant L2-index computed. Essential use is made of infinite tensor product representations of the canonical anticommutation relations algebra. 相似文献