排序方式: 共有36条查询结果,搜索用时 15 毫秒
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We discuss existence, uniqueness, and space-time Hölder regularity for solutions of the parabolic stochastic evolution equation
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Ravi P. Agarwal Donal O'Regan 《Journal of Mathematical Analysis and Applications》2008,338(2):970-983
In this paper operator-valued multiplier theorems in Banach-valued weighted Lp spaces are studied. Also weighted Sobolev-Lions type spaces are discussed when E0, E are two Banach spaces and E0 is continuously and densely embedded on E. Several conditions are found that ensure the continuity of the embedding operators that are optimally regular in these spaces in terms of interpolations of E0. These results permit us to show the separability of the anisotropic differential operators in an E-valued weighted Lp space. By using these results the maximal regularity of infinite systems of quasi elliptic partial differential equations are established. 相似文献
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Kheira Limam 《Applied mathematics and computation》2012,218(9):5605-5619
The goal of this work is to give a complete study of some abstract transmission problems (Pδ), for every δ > 0, set in unbounded domain composed of a half-line ]−∞, 0[ and a thin layer ]0, δ[. Existence and uniqueness results are obtained for strict solutions in UMD Banach spaces, by using essentially the semigroup theory and the Dore-Venni’s Theorem given in [8]. 相似文献
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Claudio Cuevas Carlos Lizama 《Journal of Difference Equations and Applications》2013,19(12):1129-1138
We characterize the discrete maximal regularity for second order difference equations by means of spectral and R-boundedness properties of the resolvent set. 相似文献
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Tuomas P. Hytönen 《Journal of Functional Analysis》2006,234(2):420-463
We establish conditions similar to the Tb theorem of David, Journé and Semmes which guarantee the boundedness of an integral transformation T with L(X)-valued kernel on , where 1<p<∞ and X is a Banach space with the unconditionality property of martingale differences (UMD). 相似文献
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Carlos Lizama 《Mathematische Nachrichten》2015,288(17-18):2079-2092
Let T be a bounded linear operator defined on a Banach space X. We introduce an operator theoretical method for linear fractional difference equations based on the notion of α‐resolvent sequence of bounded and linear operators. Then, we define and characterize the ‐ maximal regularity of solutions for the problem solely in terms of the R‐boundedness of the set 相似文献
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We study the fractional differential equation (*) Dαu(t) + BDβu(t) + Au(t) = f(t), 0 ? t ? 2π (0 ? β < α ? 2) in periodic Lebesgue spaces Lp(0, 2π; X) where X is a Banach space. Using functional calculus and operator valued Fourier multiplier theorems, we characterize, in UMD spaces, the well posedness of (*) in terms of R‐boundedness of the sets {(ik)α((ik)α + (ik)βB + A)?1}k∈ Z and {(ik)βB((ik)α + (ik)βB + A)?1}k∈ Z . Applications to the fractional problems with periodic boundary condition, which includes the time diffusion and fractional wave equations, as well as an abstract version of the Basset‐Boussinesq‐Oseen equation are treated. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
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Markus Haase 《Mathematische Zeitschrift》2009,262(2):281-299
It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(−A)1/2 generates a bounded C
0-group. The proof uses a transference principle for cosine functions.
相似文献
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