Showing papers in "Journal of Functional Analysis in 2013"

TL;DR: In this paper, the authors considered a semilinear elliptic problem and proved the existence of a positive groundstate solution of the Choquard or nonlinear Schr\"odinger--Newton equation for an optimal range of parameters.

TL;DR: In this article, a class of semilinear pseudo-parabolic equations with high initial energy J ( u 0 ) > d was studied and the invariance of some sets, global existence, nonexistence and asymptotic behavior of solutions with initial energy was shown.

TL;DR: In this paper, a stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated, and it is shown that a certain Sobolev degree of regularity is maintained, which implies continuity of solutions.

TL;DR: In this paper, the authors study the diffusive logistic equation with a free boundary in time-periodic environment and show that the spreading-vanishing dichotomy is retained in time periodic environment, and also determine the spreading speed.

TL;DR: In this article, the uniqueness of self-adjoint and Markovian extensions of the Laplacian on weighted graphs was studied and it was shown that for locally finite graphs and a certain family of metrics, completeness of the graph implies uniqueness of these extensions.

TL;DR: In this paper, a theory of Hardy spaces H L p (X ), 0 p ⩽ 1, which includes a molecular decomposition, an atomic decomposition and a square function characterization, duality of Hardy and Lipschitz spaces, and a Marcinkiewicz type interpolation theorem.

TL;DR: In this article, the authors characterize distributional chaos for linear operators on Frechet spaces in terms of a computable condition (DCC), and also as the existence of distributionally irregular vectors.

TL;DR: In this article, Leray-Schauder degree arguments and critical point theory were used for convex, lower semicontinuous perturbations of C 1 -functionals.

TL;DR: In this article, the Dirichlet problem with mean curvature operator in Minkowski space was studied and it was shown that Λ > 0 such that the problem has zero, at least one or at least two positive radial solutions according to λ ∈ ( 0, Λ ), λ = Λ or λ > Λ.

TL;DR: In this article, the authors introduce the concept of almost automorphic functions on time scales and present the first results about their basic properties, and prove a result ensuring the existence of an almost automomorphic solution for both equations, assuming that the associated homogeneous equation of this system admits an exponential dichotomy.

TL;DR: In this paper, the authors studied the global existence of weak solutions to a multi-dimensional simplified EKL system for compressible flows of nematic liquid crystals with large initial energy in a bounded domain.

TL;DR: In this article, a tracial notion of Z-absorption for simple, unital C ⁎ -algebras is studied, and it is shown that if A ≅ A ⊗ Z, then A has almost unperforated Cuntz semigroup, and if in addition A is nuclear and separable, this property is equivalent to having A ≆ A⊆ Z.

TL;DR: In this article, the authors studied the regularity properties of two maximal operators of convolution type: the heat flow maximal operator (associated to the Gauss kernel) and the Poisson maximal operator associated to the poisson kernel, and proved that these maximal operators do not increase the L p -variation of a function for any p ⩾ 1, while in dimensions d > 1, they obtain the corresponding results for the L 2 −variation.

TL;DR: In this paper, it was shown that the free orthogonal and unitary quantum groups F O N + and F U N + are weakly amenable and that their Cowling-Haagerup constant is equal to 1.

TL;DR: In this paper, a probabilistic definition of solutions of semilinear elliptic equations with (possibly nonlocal) operators associated with regular Dirichlet forms and with measure data is proposed.

TL;DR: In this paper, the authors define Dirac operators and magnetic Schrodinger Hamiltonians on fractals and prove their self-adjointness, using the concept of 1-forms and derivations associated with Dirichlet forms.

TL;DR: In this article, the authors studied the homogenization of lattice energies related to Ising systems of the form E e ( u ) = − ∑ i j c i j e u i u j e, with u i a spin variable indexed on the portion of a cubic lattice Ω ∩ e Z d, by computing their Γ-limit in the framework of surface energies in a BV setting.

TL;DR: In this article, the authors consider a multidimensional stochastic differential equation driven by a stable-like Levy process and prove that the law of the solution immediately has a density in some Besov space, under some non-degeneracy condition on the driving Levy process.

TL;DR: In this article, the spectral spectrum of weighted composition operators u C φ acting on a wide class of analytic function spaces was investigated, including Hardy spaces, Bergman spaces, and weighted Banach spaces of H ∞ -type.

TL;DR: In this paper, the celebrated Littlewood mixed norm inequality is used to prove interpolation theorems for bilinear operators defined on couples of c 0 -weighted sequence spaces generated by parameters of quasi-concave functions.

TL;DR: In this paper, it was shown that the Lipschitz-free space over doubling metric space has bounded approximation property and monotone finite-dimensional Schauder decomposition.

TL;DR: In this article, the authors define an algebra C { X i : i ∈ I } which contains polynomials and define transition operators for additive and multiplicative free convolution.

TL;DR: In this article, an addition operation on the class of quasi-concave functions is defined, which is similar to the well-known sup-convolution, but it has the property that it polarizes the Lebesgue integral.

TL;DR: In this article, the Segal-Bargmann transform has a meaningful limit Gs,t as N → ∞, which can be identified as an operator on the space of complex Laurent polynomials.

TL;DR: In this paper, the boundedness of rough Fourier integral and pseudodifferential operators, defined by general rough Hormander class amplitudes, on Banach and quasi-Banach LpLp spaces was studied.

TL;DR: In this article, the authors obtained monotonicity properties for minima and stable solutions of general energy functionals of the type ∫ F ( ∇ u, u, x ) d x under the assumption that a certain integral grows at most quadratically at infinity.

TL;DR: In this article, the existence of stable solutions of the Allen-Cahn equation whose zero sets are not hyperplanes was proved in dimension n + 1 ⩾ 8, where n is the number of vertices.

TL;DR: In this paper, the authors strengthen the result established by L. Cohen on uncertainty principle involving phase derivative and propose stronger uncertainty principles not only in the classical setting for Fourier transform, but also for self-adjoint operators.

TL;DR: The existence of global weak solutions to the Cauchy problem for the Novikov equation is established in the space C( [ 0, ∞ ) × R ) ∩ L ∞ ( [ 0, ∞ ] ; H 1 ( R ) ) without the sign condition on the initial value as discussed by the authors.

TL;DR: In this article, a dyadic model dominating the operator and an adaptation of a method of Cruz-Uribe, Martell and Perez were used to estimate the Bergman projection in weighted Bergman spaces in terms of Bekolle constant.