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1.
Sen Yang 《Comptes Rendus Mathematique》2017,355(2):211-215
By using the infinitesimal methods due to Bloch, Green, and Griffiths in [1], [4], we construct an infinitesimal form of the regulator map and verify that its kernel is , which suggests that Question 1.1 seems reasonable at the infinitesimal level. 相似文献
2.
We prove mixed -estimates, with , for higher-order elliptic and parabolic equations on the half space with general boundary conditions which satisfy the Lopatinskii–Shapiro condition. We assume that the elliptic operators A have leading coefficients which are in the class of vanishing mean oscillations both in the time variable and the space variable. In the proof, we apply and extend the techniques developed by Krylov [24] as well as Dong and Kim in [13] to produce mean oscillation estimates for equations on the half space with general boundary conditions. 相似文献
3.
We study solutions of the focusing energy-critical nonlinear heat equation in . We show that solutions emanating from initial data with energy and -norm below those of the stationary solution W are global and decay to zero, via the “concentration-compactness plus rigidity” strategy of Kenig–Merle [33], [34]. First, global such solutions are shown to dissipate to zero, using a refinement of the small data theory and the -dissipation relation. Finite-time blow-up is then ruled out using the backwards-uniqueness of Escauriaza–Seregin–Sverak [17], [18] in an argument similar to that of Kenig–Koch [32] for the Navier–Stokes equations. 相似文献
4.
5.
For an oriented 2-dimensional manifold Σ of genus g with n boundary components, the space carries the Goldman–Turaev Lie bialgebra structure defined in terms of intersections and self-intersections of curves. Its associated graded Lie bialgebra (under the natural filtration) is described by cyclic words in and carries the structure of a necklace Schedler Lie bialgebra. The isomorphism between these two structures in genus zero has been established in [13] using Kontsevich integrals and in [2] using solutions of the Kashiwara–Vergne problem.In this note, we give an elementary proof of this isomorphism over . It uses the Knizhnik–Zamolodchikov connection on . We show that the isomorphism naturally depends on the complex structure on the surface. The proof of the isomorphism for Lie brackets is a version of the classical result by Hitchin [9]. Surprisingly, it turns out that a similar proof applies to cobrackets.Furthermore, we show that the formality isomorphism constructed in this note coincides with the one defined in [2] if one uses the solution of the Kashiwara–Vergne problem corresponding to the Knizhnik–Zamolodchikov associator. 相似文献
6.
Using a modification of the invariant Jensen forcing of [11], we define a model of ZFC, in which, for a given , there exists a lightface -set of reals, which is a -equivalence class, hence a countable set, and which does not contain any OD element, while every non-empty countable -set of reals is constructible, hence contains only OD reals. 相似文献
7.
A.D. Brooke-Taylor V. Fischer S.D. Friedman D.C. Montoya 《Annals of Pure and Applied Logic》2017,168(1):37-49
We provide a model where for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties. 相似文献
8.
Haibo Cui Haiyan Yin Jinshun Zhang Changjiang Zhu 《Journal of Differential Equations》2018,264(7):4564-4602
In this paper, we are concerned with the asymptotic behavior of solutions to the system of Euler equations with time-depending damping, in particular, include the constant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Compared with previous results about Euler equations with constant coefficient damping obtained by Hsiao and Liu (1992) [2], and Nishihara (1996) [9], we obtain a general result when the initial perturbation belongs to the same space, i.e. . Our proof is based on the classical energy method. 相似文献
9.
We derive trace formulas for a pair of self-adjoint operators and H under the assumption that is in a Schatten class. This extends the trace formulas of [8], where V alone is assumed to be in a Schatten class. Our trace formulas apply, in particular, in the setting of differential operators and are based on Taylor-like approximations of operator functions. This significantly improves non-Taylor based trace formulas of [10]. 相似文献
10.
We investigate blow-up properties for the initial-boundary value problem of a Keller–Segel model with consumption of chemoattractant when the spatial dimension is three. Through a kinetic reformulation of the Keller–Segel system, we first derive some higher-order estimates and obtain certain blow-up criteria for the local classical solutions. These blow-up criteria generalize the results in [4], [5] from the whole space to the case of bounded smooth domain . Lower global blow-up estimate on is also obtained based on our higher-order estimates. Moreover, we prove local non-degeneracy for blow-up points. 相似文献
11.
12.
Len Meas 《Comptes Rendus Mathematique》2017,355(2):161-165
In this work, we will establish local in time dispersive estimates for solutions to the model-case Dirichlet wave equation inside a cylindrical convex domain with a smooth boundary . Let us recall that dispersive estimates are key ingredients to prove Strichartz estimates. Nonoptimal Strichartz estimates for waves inside an arbitrary domain Ω have been proved by Blair–Smith–Sogge [1], [2]. Better estimates in strictly convex domains have been obtained in [4]. Our case of cylindrical domains is an extension of the result of [4] in the case where the curvature radius ≥0 depends on the incident angle and vanishes in some directions. 相似文献
13.
For Toeplitz operators acting on the weighted Fock space , we consider the semi-commutator , where is a certain weight parameter that may be interpreted as Planck's constant ? in Rieffel's deformation quantization. In particular, we are interested in the semi-classical limit
()
It is well-known that tends to 0 under certain smoothness assumptions imposed on f and g. This result was recently extended to by Bauer and Coburn. We now further generalize (?) to (not necessarily bounded) uniformly continuous functions and symbols in the algebra of bounded functions having vanishing mean oscillation on . Our approach is based on the algebraic identity , where denotes the Hankel operator corresponding to the symbol g, and norm estimates in terms of the (weighted) heat transform. As a consequence, only f (or likewise only g) has to be contained in one of the above classes for (?) to vanish. For g we only have to impose , e.g. . We prove that the set of all symbols with the property that for all coincides with . Additionally, we show that holds for all . Finally, we present new examples, including bounded smooth functions, where (?) does not vanish. 相似文献
14.
In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces F_p~(α,q) (ω; R~(n_1)× R~(n_2)) based on the Frazier and Jawerth' method in [11]. This space was′firstly introduced in [18]. Then we establish its dual space and get that(F_p~(α,q))*= CMO_p~(-α,q') for 0 p ≤ 1. 相似文献
15.
Minghua Lin 《Comptes Rendus Mathematique》2018,356(7):818-822
Any positive matrix with each block square satisfies the symmetric norm inequality , where () are quantities involving the width of numerical ranges. This extends the main theorem of Bourin and Mhanna (2017) [4] to a higher number of blocks. 相似文献
16.
Neel Patel 《Journal of Differential Equations》2018,264(3):1841-1885
We consider continuation criteria for the three-dimensional relativistic Vlasov–Maxwell system. When the particle density, , is compactly supported at , we prove , where and is arbitrarily small, is a continuation criteria. Our continuation criteria is an improvement in the range to the previously best known criteria due to Kunze [7]. We also consider continuation criteria when has noncompact support. In this regime, Luk–Strain [9] proved that is a continuation criteria for . We improve this result to . Finally, we build on another result by Luk–Strain [8]. The authors proved boundedness of momentum support on a fixed two-dimensional plane is a sufficient continuation criteria. We prove the same result even if the plane varies continuously in time. 相似文献
17.
《Stochastic Processes and their Applications》2005,115(6):983-1016
We work out a stationary process on the real line to represent the positions of the multiple cracks which are observed in some composites materials submitted to a fixed unidirectional stress . Our model is the one-dimensional random sequential adsorption. We calculate the intensity of the process and the distribution of the inter-crack distance in the Palm sense. Moreover, the successive crack positions of the one-sided process (denoted by , ) are described. We prove that the sequence is a “conditional renewal process”, where is the value of the stress at which forms. The approaches “in the Palm sense” and “one-sided process” merge when . The saturation case is also investigated. 相似文献
19.
Takahiro Hashira Sachiko Ishida Tomomi Yokota 《Journal of Differential Equations》2018,264(10):6459-6485
This paper deals with the quasilinear degenerate Keller–Segel systems of parabolic–parabolic type in a ball of (). In the case of non-degenerate diffusion, Cie?lak–Stinner [3], [4] proved that if , where m denotes the intensity of diffusion and q denotes the nonlinearity, then there exist initial data such that the corresponding solution blows up in finite time. As to the case of degenerate diffusion, it is known that a solution blows up if (see Ishida–Yokota [13]); however, whether the blow-up time is finite or infinite has been unknown. This paper gives an answer to the unsolved problem. Indeed, the finite-time blow-up of energy solutions is established when . 相似文献
20.
Andrew Lorent Guanying Peng 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(2):481-516
Let be a bounded simply-connected domain. The Eikonal equation for a function has very little regularity, examples with singularities of the gradient existing on a set of positive measure are trivial to construct. With the mild additional condition of two vanishing entropies we show ?u is locally Lipschitz outside a locally finite set. Our condition is motivated by a well known problem in Calculus of Variations known as the Aviles–Giga problem. The two entropies we consider were introduced by Jin, Kohn [26], Ambrosio, DeLellis, Mantegazza [2] to study the Γ-limit of the Aviles–Giga functional. Formally if u satisfies the Eikonal equation and if
(1)
where and are the entropies introduced by Jin, Kohn [26], and Ambrosio, DeLellis, Mantegazza [2], then ?u is locally Lipschitz continuous outside a locally finite set.Condition (1) is motivated by the zero energy states of the Aviles–Giga functional. The zero energy states of the Aviles–Giga functional have been characterized by Jabin, Otto, Perthame [25]. Among other results they showed that if for some sequence and then ?u is Lipschitz continuous outside a finite set. This is essentially a corollary to their theorem that if u is a solution to the Eikonal equation a.e. and if for every “entropy” Φ (in the sense of [18], Definition 1) function u satisfies distributionally in Ω then ?u is locally Lipschitz continuous outside a locally finite set. In this paper we generalize this result in that we require only two entropies to vanish.The method of proof is to transform any solution of the Eikonal equation satisfying (1) into a differential inclusion where is a connected compact set of matrices without Rank-1 connections. Equivalently this differential inclusion can be written as a constrained non-linear Beltrami equation. The set K is also non-elliptic in the sense of Sverak [32]. By use of this transformation and by utilizing ideas from the work on regularity of solutions of the Eikonal equation in fractional Sobolev space by Ignat [23], DeLellis, Ignat [15] as well as methods of Sverak [32], regularity is established. 相似文献