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991.
We introduce new reproducing kernel Hilbert spaces on a semi-infinite domain and demonstrate existence and uniqueness of solutions to the nonhomogeneous telegraph equation in these spaces if the driver is square-integrable and sufficiently smooth. 相似文献
992.
Benjamin C. Pooley 《Journal of Differential Equations》2018,264(8):5180-5196
It is known that in a classical setting, the Navier–Stokes equations can be reformulated in terms of so-called magnetization variables w that satisfy
(1)
and relate to the velocity u via a Leray projection . We will prove the equivalence of these formulations in the setting of weak solutions that are also in on the 3-dimensional torus.Our main focus is the proof of global well-posedness in for a new variant of (1), where is replaced by w in the second nonlinear term:(2)
This is based on a maximum principle, analogous to a similar property of the Burgers equations. 相似文献
993.
B. M. Braga 《Journal of Functional Analysis》2018,274(11):3149-3169
In this paper, we study nonlinear embeddings between Banach spaces. More specifically, the goal of this paper is to study weaker versions of coarse and uniform embeddability, and to provide suggestive evidences that those weaker embeddings may be stronger than one would think. We do such by proving that many known results regarding coarse and uniform embeddability remain valid for those weaker notions of embeddability. 相似文献
994.
A new geometric property of Banach spaces recently introduced by G. Kasparov and G. Yu, called Property (H), has important applications to the strong Novikov conjecture and the coarse Novikov conjecture, yet is far from being well understood. In this paper, we investigate various uniformly continuous maps on unit spheres of Banach spaces and prove that all separable Banach lattices with nontrivial cotype have Property (H). 相似文献
995.
《Mathematische Nachrichten》2018,291(2-3):492-517
We study the existence of nonnegative and nonzero solutions for the following class of quasilinear Schrödinger equations: where V and Q are potentials that can be singular at the origin, unbounded or vanishing at infinity. In order to prove our existence result we used minimax techniques in a suitable weighted Orlicz space together with regularity arguments and we need to obtain a symmetric criticality type result. 相似文献
996.
《Mathematische Nachrichten》2018,291(2-3):284-325
In this article, the authors characterize higher‐order Sobolev spaces , with , and , or with , and , via the Lusin area function and the Littlewood–Paley ‐function in terms of ball averages, where denotes the maximal integer not greater than . Moreover, the authors also complement the above results in the endpoint cases of p via establishing some weak type estimates. These improve and develop the corresponding known results for Sobolev spaces with smoothness order . 相似文献
997.
《Mathematische Nachrichten》2018,291(11-12):1743-1756
The paper deals with the possibly degenerate behaviour of the exterior derivative operator defined on 1‐forms on metric measure spaces. The main examples we consider are the non self‐similar Sierpinski carpets recently introduced by Mackay, Tyson and Wildrick. Although topologically one‐dimensional, they may have positive two‐dimensional Lebesgue measure and carry nontrivial 2‐forms. We prove that in this case the curl operator (and therefore also the exterior derivative on 1‐forms) is not closable, and that its adjoint operator has a trivial domain. We also formulate a similar more abstract result. It states that for spaces that are, in a certain way, structurally similar to Sierpinski carpets, the exterior derivative operator taking 1‐forms into 2‐forms cannot be closable if the martingale dimension is larger than one. 相似文献
998.
《Mathematische Nachrichten》2018,291(10):1514-1532
Necessary and sufficient conditions for uniform rotundity of Orlicz function spaces equipped with the p‐Amemiya norm are presented. The obtained results unify, complete and widen the characterization of uniform rotundity of Orlicz spaces. In the case of the ∞‐Amemiya (i.e. the Luxemburg) norm or the 1‐Amemiya (i.e. the Orlicz) norm, these results were known earlier. Some connections with the fixed point theory and the best approximation theory are presented. 相似文献
999.
《Mathematische Nachrichten》2018,291(13):2024-2044
In this paper we study the maximal function and local means characterizations and the non‐smooth atomic decomposition of the Triebel–Lizorkin type spaces with variable exponents . These spaces were recently introduced by Yang et al. and cover the Triebel–Lizorkin spaces with variable exponents as well as the classical Triebel–Lizorkin spaces , even the case when . Moreover, covered by this scale are also the Triebel–Lizorkin‐type spaces with constant exponents which, in turn cover the Triebel–Lizorkin–Morrey spaces. As an application we obtain a pointwise multiplier assertion for those spaces. 相似文献
1000.
We give a -approximation algorithm for minimizing total weighted completion time on a single machine under release time and precedence constraints. This settles a recent conjecture on the approximability of this scheduling problem (Skutella, 2016). 相似文献