Some capacities and applications - the lemma on mixed derivatives revisited
J. Korevaar (1986)
Matematički Vesnik
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J. Korevaar (1986)
Matematički Vesnik
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Winfried Sickel (2006)
Banach Center Publications
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We investigate the convergence and the rate of convergence in , 1 < p < ∞, of a bivariate interpolating (with respect to a sparse grid) trigonometric polynomial in the framework of Sobolev spaces of dominating mixed smoothness.
Guangbin Ren, Jihuai Shi (2004)
Studia Mathematica
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For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space of the polydisc onto the mixed norm space of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.
Zuliang Lu (2016)
Applications of Mathematics
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We study new a posteriori error estimates of the mixed finite element methods for general optimal control problems governed by nonlinear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates in -norm and -norm for both the state, the co-state and the control approximation. Such estimates, which seem to be new,...
Philippe Eyssidieux, Carlos Simpson (2011)
Journal of the European Mathematical Society
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Let be a compact Kähler manifold, be a base point and be the monodromy representation of a -VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at and a variation of mixed Hodge structures whose monodromy is the universal deformation of .
Ewa Zadrzyńska
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CONTENTS1. Introduction....................................................................................................................................................52. Notations and preliminaries .........................................................................................................................11 2.1. Function spaces and spaces of distributions............................................................................................11 2.2. Perturbations...
Bogdan Rzepecki (1975)
Annales Polonici Mathematici
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W. Mlak (1963)
Annales Polonici Mathematici
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Březina, Jan
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Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.
Zhiting Xu (2010)
Annales Polonici Mathematici
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Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations ⎧ , ⎨ ⎩ under quite general conditions. These results are extensions of the recent results of Sun and Wong, [J. Math. Anal. Appl. 334 (2007)] and Zheng, Wang and Han [Appl. Math. Lett. 22 (2009)] for forced second order ordinary differential equations with mixed nonlinearities, and include some known oscillation results in the literature
C. Johnson (1976)
Publications mathématiques et informatique de Rennes
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Denny H. Leung, Wee-Kee Tang (2006)
Studia Mathematica
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We investigate the existence of higher order ℓ¹-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space : (1) Every block subspace of X contains an -spreading model, (2) The Bourgain ℓ¹-index for any block subspace Y of X, (3) and every block subspace Y of X contains a block sequence equivalent to a subsequence of the unit vector basis of X. Moreover, if one (and hence all) of these...
D. Radunović (1989)
Matematički Vesnik
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Lev Markhasin (2015)
Acta Arithmetica
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Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the -discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with...
Rolf Stenberg (1988)
Numerische Mathematik
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Joanna Janczewska (2011)
Annales Polonici Mathematici
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We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: , where t ∈ ℝ, q ∈ ℝⁿ and T>0 is a fixed positive number. By an almost homoclinic solution (to 0) we mean one that joins 0 to itself and q ≡ 0 may not be a stationary point. We assume that V and u are T-periodic with respect to the time variable, V is C¹-smooth and u is continuous. Moreover, f is non-zero, bounded, continuous and square-integrable....
Jan Vybiral
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We study several techniques which are well known in the case of Besov and Triebel-Lizorkin spaces and extend them to spaces with dominating mixed smoothness. We use the ideas of Triebel to prove three important decomposition theorems. We deal with so-called atomic, subatomic and wavelet decompositions. All these theorems have much in common. Roughly speaking, they say that a function f belongs to some function space (say ) if, and only if, it can be decomposed as , convergence in S’, with...