Corrigendum to: parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces
Vagif S. Guliyev, Mehriban N. Omarova (2016)
Open Mathematics
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Vagif S. Guliyev, Mehriban N. Omarova (2016)
Open Mathematics
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Adam Kubica, Wojciech M. Zajączkowski (2007)
Applicationes Mathematicae
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We examine the regularity of solutions of a certain parabolic system in the weighted Sobolev space , where the weight is of the form , r is the distance from a distinguished axis and μ ∈ (0,1).
Lotfi Riahi (2003)
Colloquium Mathematicae
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We prove global pointwise estimates for the Green function of a parabolic operator with potential in the parabolic Kato class on a cylindrical domain Ω. We apply these estimates to obtain a new and shorter proof of the Harnack inequality [16], and to study the boundary behavior of nonnegative solutions.
Martino Prizzi (2003)
Fundamenta Mathematicae
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We consider the parabolic equation (P) , (t,x) ∈ ℝ₊ × ℝⁿ, and the corresponding semiflow π in the phase space H¹. We give conditions on the nonlinearity F(x,u), ensuring that all bounded sets of H¹ are π-admissible in the sense of Rybakowski. If F(x,u) is asymptotically linear, under appropriate non-resonance conditions, we use Conley’s index theory to prove the existence of nontrivial equilibria of (P) and of heteroclinic trajectories joining some of these equilibria. The results obtained...
Tuomo Kuusi, Giuseppe Mingione (2014)
Journal of the European Mathematical Society
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The spatial gradient of solutions to non-homogeneous and degenerate parabolic equations of -Laplacean type can be pointwise estimated by natural Wolff potentials of the right hand side measure.
Amiran Gogatishvili, Luboš Pick, Filip Soudský (2014)
Studia Mathematica
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We characterize associate spaces of weighted Lorentz spaces GΓ(p,m,w) and present some applications of this result including necessary and sufficient conditions for a Sobolev-type embedding into .
Cung The Anh, Nguyen Van Quang (2010)
Annales Polonici Mathematici
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We consider the first initial boundary value problem for nonautonomous quasilinear degenerate parabolic equations involving weighted p-Laplacian operators, in which the nonlinearity satisfies the polynomial condition of arbitrary order and the external force is normal. Using the asymptotic a priori estimate method, we prove the existence of uniform attractors for this problem. The results, in particular, improve some recent ones for nonautonomous p-Laplacian equations.
Mohammed Ali, Mohammed Al-Dolat (2016)
Open Mathematics
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In this paper, we study the the parabolic Marcinkiewicz integral [...] MΩ,hρ1,ρ2 on product domains Rn × Rm (n, m ≥ 2). Lp estimates of such operators are obtained under weak conditions on the kernels. These estimates allow us to use an extrapolation argument to obtain some new and improved results on parabolic Marcinkiewicz integral operators.
Dorothee D. Haroske, Philipp Skandera (2014)
Banach Center Publications
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We study continuous embeddings of Besov spaces of type , where s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞, and the weight w is doubling. This approach generalises recent results about embeddings of Muckenhoupt weighted Besov spaces. Our main argument relies on appropriate atomic decomposition techniques of such weighted spaces; here we benefit from earlier results by Bownik. In addition, we discuss some other related weight classes briefly and compare corresponding results.
Elke Wolf (2011)
Annales Polonici Mathematici
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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ
Benny Avelin, Ugo Gianazza, Sandro Salsa (2016)
Journal of the European Mathematical Society
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We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic -Laplacian equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of...
Elke Wolf (2009)
Annales Polonici Mathematici
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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator acting between weighted Banach spaces of holomorphic functions and weighted Bloch type spaces. Under some assumptions on the weights we give a necessary as well as a sufficient condition for such an operator to be bounded resp. compact.
Guillermo Reyes, Juan Luis Vázquez (2006)
Journal of the European Mathematical Society
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In the theory of elliptic equations, the technique of Schwarz symmetrization is one of the tools used to obtain a priori bounds for classical and weak solutions in terms of general information on the data. A basic result says that, in the absence of lower-order terms, the symmetric rearrangement of the solution of an elliptic equation, that we write , can be compared pointwise with the solution of the symmetrized problem. The main question we address here is the modification of the...
Eva A. Gallardo-Gutiérrez, Jonathan R. Partington (2013)
Annales de l’institut Fourier
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A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on by means of an integral with respect to a measure. In particular, we show the existence of a family of measures which represents the adjoint of a weighted composition operator under fairly mild assumptions, and we discuss not only uniqueness but also the generalization of Aleksandrov–Clark measures which corresponds to the unweighted case, that is, to the...
W. M. Zajączkowski (2007)
Applicationes Mathematicae
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We consider the nonstationary Stokes system with slip boundary conditions in a bounded domain which contains some distinguished axis. We assume that the data functions belong to weighted Sobolev spaces with the weight equal to some power function of the distance to the axis. The aim is to prove the existence of solutions in corresponding weighted Sobolev spaces. The proof is divided into three parts. In the first, the existence in 2d in weighted spaces near the axis is shown. In the...
Caroline Sweezy (1998)
Studia Mathematica
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If Ω is a Lip(1,1/2) domain, μ a doubling measure on , i = 0,1, are two parabolic-type operators with coefficients bounded and measurable, 2 ≤ q < ∞, then the associated measures , have the property that implies is absolutely continuous with respect to whenever a certain Carleson-type condition holds on the difference function of the coefficients of and . Also implies whenever both measures are center-doubling measures. This is B. Dahlberg’s result for elliptic measures...
Wolf von Wahl (1983)
Annales Polonici Mathematici
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