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1.
In this paper, we study quasilinear elliptic equations with the nonlinearity modelled after the -Laplacian on nonsmooth domains and obtain sharp Calderón–Zygmund type estimates in the variable exponent setting. In a recent work of [12], the estimates obtained were strictly above the natural exponent and hence there was a gap between the natural energy estimates and estimates above , see (1.3) and (1.4). Here, we bridge this gap to obtain the end point case of the estimates obtained in [12], see (1.5). In order to do this, we have to obtain significantly improved a priori estimates below , which is the main contribution of this paper. We also improve upon the previous results by obtaining the estimates for a larger class of domains than what was considered in the literature. 相似文献
2.
Following the approach and the terminology introduced in Deya and Schott (2013) [6], we construct a product Lévy area above the q-Brownian motion (for ) and use this object to study differential equations driven by the process.We also provide a detailed comparison between the resulting “rough” integral and the stochastic “Itô” integral exhibited by Donati-Martin (2003) [7]. 相似文献
3.
In [6], it was asked whether all flat holomorphic Cartan geometries on a complex torus are translation invariant. We answer this affirmatively under the assumption that the complex Lie group G is affine. More precisely, we show that every holomorphic Cartan geometry of type , with G a complex affine Lie group, on any complex torus is translation invariant. 相似文献
4.
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
5.
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
6.
7.
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
8.
Let G be a reductive group scheme of type A acting on a spherical scheme X. We prove that there exists a number C such that the multiplicity is bounded by C, for any finite field F and any irreducible representation ρ of . We give an explicit bound for C. We conjecture that this result is true for any reductive group scheme and when F ranges (in addition) over all local fields of characteristic 0.Different aspects of this conjecture were studied in [3], [11], [6], [7]. 相似文献
9.
Gregory Duran Cunha 《Journal of Pure and Applied Algebra》2018,222(10):2964-2974
In the projective plane over a finite field of order q, a Tallini curve is a plane irreducible (algebraic) curve of (minimum) degree containing all points of . Such curves were investigated by G. Tallini [8], [9] in 1961, and by Homma and Kim [5] in 2013. Our results concern the automorphism groups, the Weierstrass semigroups, the Hasse–Witt invariants, and quotient curves of the Tallini curves. 相似文献
10.
11.
(1) Let R be an affine algebra over an algebraically closed field of characteristic 0 with . Let P be a projective -module of rank n with determinant L. Suppose I is an ideal of A of height n such that there are two surjections and . Assume that either (a) and or (b) k is arbitrary but is even. Then P has a unimodular element (see 4.1, 4.3).(2) Let R be a ring containing of even dimension n with height of the Jacobson radical of . Let P be a projective -module of rank n with trivial determinant. Assume that there exists a surjection , where is an ideal of height n such that I is generated by n elements. Then P has a unimodular element (see 3.4). 相似文献
12.
Alexander Tsymbaliuk 《Journal of Pure and Applied Algebra》2017,221(10):2633-2646
In this short article, we compute the classical limits of the quantum toroidal and affine Yangian algebras of by generalizing our arguments for from [7] (an alternative proof for is given in [10]). We also discuss some consequences of these results. 相似文献
13.
Let G be a complex linear algebraic group, its Lie algebra and a nilpotent element. Vust's Theorem says that in case of , the algebra , where is the stabilizer of e under the adjoint action, is generated by the image of the natural action of d-th symmetric group and the linear maps . In this paper, we give an analogue of Vust's Theorem for and when the nilpotent elements e satisfy that is normal. As an application, we study the higher Schur–Weyl duality in the sense of [4] for types B, C and D, which establishes a relationship between W-algebras and degenerate affine braid algebras. 相似文献
14.
Pradeep K. Rai 《Journal of Pure and Applied Algebra》2018,222(2):316-322
Let G be a special p-group minimally generated by elements and having derived subgroup of order . Berkovich asked to find the Schur multiplier and covering groups of such groups G Berkovich and Janko (2011) [1]. We try to give an answer to this question in this article. 相似文献
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16.
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
17.
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
18.
Sumana Hatui L.R. Vermani Manoj K. Yadav 《Journal of Pure and Applied Algebra》2018,222(10):3293-3302
Let G be a central product of two groups H and K. We study second cohomology group of G, having coefficients in a divisible abelian group D with trivial G-action, in terms of the second cohomology groups of certain quotients of H and K. In particular, for , some of our results provide a refinement of results from Wiegold (1971) [10] and Eckmann et al. (1973) [2]. 相似文献
19.
Richard Gratwick Aidys Sedipkov Mikhail Sychev Aris Tersenov 《Comptes Rendus Mathematique》2017,355(3):359-362
In this paper, we prove that if , and , , then all problems (1), (2) admit solutions in the class , which are in fact -regular provided there are no pathological solutions to the Euler equation (5). Here is called a pathological solution to equation (5) if the equation holds in , as , and . We also prove that the lack of pathological solutions to the Euler equation results in the lack of the Lavrentiev phenomenon, see Theorem 9; no growth assumptions from below are required in this result. 相似文献
20.
Samaria Montenegro 《Annals of Pure and Applied Logic》2017,168(1):191-232
The main result of this paper is a positive answer to the Conjecture 5.1 of [14] by A. Chernikov, I. Kaplan and P. Simon: If M is a PRC field, then is NTP2 if and only if M is bounded. In the case of PpC fields, we prove that if M is a bounded PpC field, then is NTP2. We also generalize this result to obtain that, if M is a bounded PRC or PpC field with exactly n orders or p-adic valuations respectively, then is strong of burden n. This also allows us to explicitly compute the burden of types, and to describe forking. 相似文献