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Start Over Subject regularity

1. A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

Creator:
Neustupa, Jiří
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Navier-Stokes equation, suitable weak solution, and regularity
Language:
English
Description:
We deal with a suitable weak solution (v, p) to the Navier-Stokes equations in a domain Ω ⊂ R 3 . We refine the criterion for the local regularity of this solution at the point (fx0, t0), which uses the L 3 -norm of v and the L 3/2 -norm of p in a shrinking backward parabolic neighbourhood of (x0, t0). The refinement consists in the fact that only the values of v, respectively p, in the exterior of a space-time paraboloid with vertex at (x0, t0), respectively in a ''small'' subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point (x0, t0) if v and p are “smooth” outside the paraboloid.
Rights:
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2. Complex uncertain interfaces

Creator:
Votruba, Zdeněk and Novák , Mirko
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Systems interface, hybrid system, interface dimension, system uncertainty, regularity, reliability, and system analysis
Language:
English
Description:
Both Scientists and System Analytics share common experience that complex interfaces (for example "human - machine" interface within the complex hybrid system, or synapse in the human brain) susceptibly react both to the dimension of the task (i.e.: the number / type of interface parameters / markers) and to the degree of uncertainty. In order to quantitatively evaluate this effect, the model of interface is presented first. Then the problem is analyzed. The results of the study indicate: Even a low degree of uncertainty, "acting" homogeneously on all parameters of the respective interface, has significantly adverse effect on the interface regularity (consequently the reliability of systems processes as well) if the number of parameters (i.e. dimension of the pertinent task) is sufficiently high. Even a significant uncertainty in one or in a small number (typically 1 or 2) of interface parameters has a limited or negligible impact on the interface regularity if this interface is sufficiently robust. There are three basic attempts how to increase the regularity of complex interfaces: (a) smart simplification (b) utilizing redundancy or contextuality (c) interface conjugation.
Rights:
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3. Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition

Creator:
Amrouche, Cherif and Nečasová, Šárka
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
the Laplace equation, weighted Sobolev spaces, the half space, existence, uniqueness, and regularity
Language:
English
Description:
We deal with the Laplace equation in the half space. The use of a special family of weigted Sobolev spaces as a framework is at the heart of our approach. A complete class of existence, uniqueness and regularity results is obtained for inhomogeneous Dirichlet problem.
Rights:
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4. On Hölder regularity for vector-valued minimizers of quasilinear functionals

Creator:
Daněček, Josef and Viszus, Eugen
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
quasilinear functional, minimizer, regularity, and Campanato-Morrey space
Language:
English
Description:
We discuss the interior Hölder everywhere regularity for minimizers of quasilinear functionals of the type A(u; Ω) = Z Ω A αβ ij (x,u)Dαu iDβu j dx whose gradients belong to the Morrey space L 2,n−2 (Ω, RnN ).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. On the continuity of minimizers for quasilinear functionals

Creator:
Cruz-Uribe, David, Di Gironimo, Patrizia, and D´Onofrio, Luigi
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
regularity, quasilinear functionals, and calculus of variations
Language:
English
Description:
In this paper we establish a continuity result for local minimizers of some quasilinear functionals that satisfy degenerate elliptic bounds. The non-negative function which measures the degree of degeneracy is assumed to be exponentially integrable. The minimizers are shown to have a modulus of continuity controlled by $\log \log (1/|x|)^{-1}$. Our proof adapts ideas developed for solutions of degenerate elliptic equations by J. Onninen, X. Zhong: Continuity of solutions of linear, degenerate elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), 103–116.
Rights:
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6. Semiregularity of congruences implies congruence modularity at 0

Creator:
Chajda, Ivan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
regularity, modularity, semiregularity, and modularity at 0
Language:
English
Description:
We introduce a weakened form of regularity, the so called semiregularity, and we show that if every diagonal subalgebra of $\mathcal A \times \mathcal A$ is semiregular then $\mathcal A$ is congruence modular at 0.
Rights:
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7. Sequential retractivities and regularity on inductive limits

Creator:
Qiu, Jing-Hui
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
inductive limits, regularity, and sequential retractivities
Language:
English
Description:
In this paper we prove the following result: an inductive limit $(E,t) = \text{ind}(E_n,t_n)$ is regular if and only if for each Mackey null sequence $(x_k)$ in $(E,t)$ there exists $n=n(x_k)\in \mathbb N$ such that $(x_k)$ is contained and bounded in $(E_n,t_n)$. From this we obtain a number of equivalent descriptions of regularity.
Rights:
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8. Some concepts of regularity for parametric multiple-integral problems in the calculus of variations

Creator:
Crampin, M. and Saunders, D. J.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
parametric variational problem, regularity, and multisymplectic
Language:
English
Description:
We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter $(m+1)$-form are holonomic.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

9. Uniformity of congruences in coherent varieties

Creator:
Chajda, Ivan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
uniformity, regularity, permutability, coherence, transferable congruences, and Mal'cev condition
Language:
English
Description:
An algebra A is uniform if for each ∅ ∈ Con A, every two classes of ∅ have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public