Search results for "Bounded"
showing 10 items of 658 documents
Global Lp -integrability of the derivative of a quasiconformal mapping
1988
Let f be a quasiconformal mapping of an open bounded set U in Rn into Rn . Then f′ belongs to Lp(U) for some p > n provided that f satisfies (a) U is a uniform domain and fU is a John domain or (b) f is quasisymmetric and U satisfies a metric plumpness condition.
Elliptic equations and maps of bounded length distortion
1988
On considere l'equation elliptique d'ordre 2: L(u)=Σ i,f=1 n ∂ 1 (a ij ∂ ju )=0 ou les coefficients a ij sont des fonctions C 1 dans un domaine D de R n
The tusk condition and Petrovskiĭ criterion for the normalized p‐parabolic equation
2019
We study boundary regularity for the normalized p-parabolic equation in arbitrary bounded domains. Effros and Kazdan (Indiana Univ. Math. J. 20 (1970) 683-693) showed that the so-called tusk condit ...
Vertical versus horizontal Sobolev spaces
2020
Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi f$ belongs to the Euclidean Sobolev space $S^{p}_{\alpha}(\mathbb{R}^{2n + 1})$ for any test function $\varphi$. In short, $S^{p}_{2\alpha}(\mathbb{H}^{n}) \subset S^{p}_{\alpha,\mathrm{loc}}(\mathbb{R}^{2n + 1})$. We show that the localisation can be omitted if one only cares for Sobolev regularity in the vertical direction: the horizontal Sobolev space $S_{2\alpha}^{p}(\mathbb{H}^{n})$ is continuously contained in the vertical Sobolev sp…
Restricted compositions and permutations: from old to new Gray codes
2011
Any Gray code for a set of combinatorial objects defines a total order relation on this set: x is less than y if and only if y occurs after x in the Gray code list. Let @? denote the order relation induced by the classical Gray code for the product set (the natural extension of the Binary Reflected Gray Code to k-ary tuples). The restriction of @? to the set of compositions and bounded compositions gives known Gray codes for those sets. Here we show that @? restricted to the set of bounded compositions of an interval yields still a Gray code. An n-composition of an interval is an n-tuple of integers whose sum lies between two integers; and the set of bounded n-compositions of an interval si…
Quaternary marine and continental unconformity-bounded stratigraphic units of the NW Sicily coastal belt
2017
In the coastal sector of NW Sicily, the regional correlation of relevant unconformities recognised within the Quaternary sedimentary successions allowed the mapping of seven unconformity-bounded stratigraphic units (UBSUs). The regional unconformities are marine or subaerial erosional surfaces, as well as non-depositional surfaces, locally marked by paleosoils. The erosional surfaces were produced from marine abrasion, surface water overland/concentrated flow, river erosion, karst solution, mass movement, or wind erosion. The main lithofacies of the Quaternary UBSUs consist of: (a) marine and coastal bioclastic calcarenites, (b) aeolian sandstones, (c) river deposits, (d) colluvial deposits…
Adaptive Asymptotically Tracking Control for Uncertain Strict-Feedback Nonlinear Systems with Input Quantization
2018
In this paper, we investigate the output tracking control problem for a class of uncertain nonlinear systems in parametric strict feedback form with quantized input. A novel backstepping based adaptive quantized control scheme is proposed. Different from the existing results, the true quantization parameters are allowed to be unknown in the design of adaptive controller. It is shown that with the proposed control scheme, the system output can track the desired trajectory asymptotically and all the closed-loop signals are globally uniformly bounded.
Distributed Adaptive Consensus Tracking Control of Uncertain High-order Nonlinear Systems under Directed Graph Condition
2018
In this paper, we investigate the output consensus tracking problem for a class of high-order nonlinear systems subjected to unknown parameters and uncertain external disturbances. A novel backstepping based distributed adaptive control scheme is presented under the directed communication status. For the subsystems without direct access to time-varying desired trajectory, local estimators are introduced and the corresponding adaptive laws are designed in a totally distributed fashion. With the presented scheme, the assumption on linearly parameterized reference signal and the information exchange operation of subsystem inputs in the existing results are no longer needed. It is shown that al…
Adaptive Backstepping Control of Nonlinear Uncertain Systems With Quantized States
2019
This paper investigates the stabilization problem for uncertain nonlinear systems with quantized states. All states in the system are quantized by a static bounded quantizer, including uniform quantizer, hysteresis-uniform quantizer, and logarithmic-uniform quantizer as examples. An adaptive backstepping-based control algorithm, which can handle discontinuity, resulted from the state quantization and a new approach to stability analysis are developed by constructing a new compensation scheme for the effects of the state quantization. Besides showing the global ultimate boundedness of the system, the stabilization error performance is also established and can be improved by appropriately adj…
Distributed adaptive leader–follower and leaderless consensus control of a class of strict-feedback nonlinear systems : a unified approach
2020
In this paper, distributed adaptive consensus for a class of strict-feedback nonlinear systems under directed topology condition is investigated. Both leader–follower and leaderless cases are considered in a unified framework. To design distributed controller for each subsystem, a local compensatory variable is generated based on the signals collected from its neighbors. Such a technique enables us to solve the leader–follower consensus and leaderless consensus problems in a unified framework. And it further allows us to treat the leaderless consensus as a special case of the leader–follower consensus. For leader–follower consensus, the assumption that the leader trajectory is linearly para…