Showing papers in "Journal of Functional Analysis in 2009"
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TL;DR: In this article, the authors define the Ricci curvature of metric spaces in terms of how much small balls are closer (in Wasserstein transportation distance) than their centers are.
728 citations
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TL;DR: In this article, Li et al. developed an approach to find ground state solutions, i.e., nontrivial solutions with least possible energy, based on a direct reduction of the indefinite variational problem to a definite one.
431 citations
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TL;DR: In this article, the authors studied the symmetry properties of non-local boundary reaction equations and derived a geometric formula of Poincare-type for stable solutions, from which they derived a symmetry result in the spirit of a conjecture of De Giorgi.
276 citations
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TL;DR: In this article, a new sharp affine L p Sobolev inequality for functions on R n was established, which strengthened and implies the previously known affine l p Sobolov inequality.
228 citations
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TL;DR: In this paper, the authors introduce Triebel-Lizorkin spaces with variable smoothness and integrability, and derive molecular and atomic decomposition results and show that their space is well-defined, independent of the choice of basis functions.
211 citations
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TL;DR: In this article, an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp's volume form introduced by Montgomery, was presented.
181 citations
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TL;DR: In this paper, a module analogue of locally convex vector spaces, namely locally L0-convex modules, is established and hyperplane separation theorems are proved.
150 citations
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TL;DR: In this article, the cubic defocusing fourth-order Schrodinger equation is investigated for arbitrary initial data in arbitrary space dimension Rn and it is shown that the equation is globally wellposed when n⩽8 and ill-posed whenn⩾9.
128 citations
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TL;DR: In this paper, the Dirichlet boundary conditions for radially symmetric solutions of the nonlinear heat equation were studied and various characterizations of type I and type II blowups were established.
117 citations
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TL;DR: In this article, it was shown that any partial isometry on a Hilbert space of dimension ⩽4 is complex symmetric, i.e., there exists a conjugate-linear, isometric involution C:H→H so that T=CT∗C.
115 citations
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TL;DR: In this article, the authors studied the existence, nonexistence and multiplicity of positive solutions for a family of nonlinearities of the Ambrosetti-Brezis-Cerami type in a more general form.
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TL;DR: In this paper, Sturm et al. introduced and studied rough curvature bounds for discrete spaces and graphs, and showed that the metric measure space which is approximated by a sequence of discrete spaces with rough curvatures ⩾ K will have curvature K in the sense of [J. Lott, C.Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. I, Acta Math.
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TL;DR: In this paper, the eigenvalues of non-selfadjoint unbounded operators obtained from selfadjoint operators by a perturbation that is relatively-Schatten were shown to be bounded.
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TL;DR: For α∈[1,2] and α ∈(0,1) the same operator was considered in this paper, where the ∇f term was omitted and it was shown that any solution u to Lu=f will be in Cα+β if f∈Cβ.
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TL;DR: In this article, the authors considered stochastic equations in Hilbert spaces with singular drift and proved regularizing and ultraboundedness properties of the transition semigroup and showed that the corresponding Kolmogorov operator has at most one infinitesimally invariant measure.
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TL;DR: In this article, the authors consider solutions to the linear wave equation in the exterior of a fixed black hole space-time of this type and show that for solutions with initial data which decay at infinity and at the bifurcation sphere, a weighted L 6 norm in space decays like t − 1 3.
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TL;DR: In this paper, a non-commutative Calderon-zygmund decomposition of matrix-valued functions has been studied in the context of the weak type (1, 1 ) boundedness of singular integrals.
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TL;DR: In this article, it was shown that the spatial quadratic average of all fractional derivatives of u is bounded independently of L. In particular, the time-space average ǫ(ǫ|∂x|αu)2ǫ is observed to be bounded independent of L, and this is the first result in favor of an extensive behavior up to a logarithm.
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TL;DR: In this article, the authors unify Littlewood's classical 4/3 inequality together with its m -linear extension due to Bohnenblust and Hille (which originally settled Bohr's absolute convergence problem for Dirichlet series) with a scale of inequalties of Bennett and Carl in l p -spaces.
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TL;DR: In this paper, the authors studied the initial value boundary problems of two types of nonlinear dispersive wave equations on the half-line and on a finite interval subject to homogeneous Dirichlet boundary conditions.
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TL;DR: In this article, the authors proved uniqueness for the Dirichlet problem for the complex Monge-Ampere equation on compact Kahler manifolds in the case of probability measures vanishing on pluripolar sets using the mass concentration technique due to Kolodziej coupled with inequalities for mixed monge-ampere measures and the comparison principle.
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TL;DR: Bakry and Emery as mentioned in this paper used Lyapunov functions to obtain functional inequalities which are stronger than Poincare inequalities (for instance logarithmic Sobolev or F-Sobolev).
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TL;DR: In this article, the boundary value problem for the incompressible inhomogeneous Navier-Stokes equations in the half-space was solved in the case of small data with critical regularity.
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TL;DR: In this article, the authors considered the stability of non-convolutional operators of the Sjostrand class and showed that the lp-stability of these operators is equivalent to each other.
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TL;DR: In this paper, the authors prove infinite-dimensional second order Poincare inequalities on Wiener space, thus closing a circle of ideas linking limit theorems for functionals of Gaussian fields, Stein's method and Malliavin calculus.
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TL;DR: In this paper, the quasilinear equation at critical growth admits a nontrivial weak solution u∈W01,p(Ω) for any λ⩾λ1.
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TL;DR: In this paper, the authors give a complete description of all derivations on the above algebras of operators in the case of type I von Neumann algebra M. In particular, if M is of type i ∞ then every derivation on LS(M) (resp. S(M,τ) ) is inner.
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TL;DR: In this article, a quantum group analogue of the group of orientation-preserving Riemannian isometries of a R-twisted and of compact type spectral triple is presented.
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TL;DR: In this paper, the authors investigated the solvability, regularity and vanishing viscosity limit of the 3D viscous magnetohydrodynamic system in a class of bounded domains with a slip boundary condition.
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TL;DR: In this article, it was shown that the Ricci curvatures of the second fundamental form of a Riemannian manifold can be bounded below a positive constant by a constant constant c. The first non-zero eigenvalues of the above problems were denoted by p 1 and q 1, respectively, with equality holding if and only if Ω is isometric to an n -dimensional Euclidean ball of radius 1 c.