Results 41 to 50 of about 4,705,780 (288)
On three-dimensional Hall-magnetohydrodynamic equations with partial dissipation
Boundary Value Problems, 2022 In this paper, we address the Hall-MHD equations with partial dissipation. Applying some important inequalities (such as the logarithmic Sobolev inequality using BMO space, bilinear estimates in BMO space, Young’s inequality, cancellation property ...
Baoying Du
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Concerning the pathological set in the context of probabilistic well-posedness
Comptes Rendus. Mathématique, 2021 We prove a complementary result to the probabilistic well-posedness for the nonlinear wave equation. More precisely, we show that there is a dense set $S$ of the Sobolev space of super-critical regularity such that (in sharp contrast with the ...
Sun, Chenmin, Tzvetkov, Nikolay
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Sobolev spaces on warped products [PDF]
Journal of Functional Analysis, 2018 Corrected few typos in the previous version and updated the ...
Gigli, Nicola, Han, Bang-Xian
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, 2010 In this paper, we consider in R n the Cauchy problem for the nonlinear Schrodinger equation with initial data in the Sobolev space W s,p for p n(1 ― 1/p). Moreover, we show that in one space dimension, the problem is locally well posed in L P for any 1 <
Yi Zhou
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Anisotropic Sobolev Spaces with Weights
Tokyo Journal of Mathematics, 2023 We study Sobolev spaces with weights in the half-space $\mathbb{R}^{N+1}_+=\{(x,y): x \in \mathbb{R}^N, y>0\}$, adapted to the singular elliptic operators \begin{equation*} \mathcal L =y^{ _1} _{x} +y^{ _2}\left(D_{yy}+\frac{c}{y}D_y -\frac{b}{y^2}\right). \end{equation*}
Metafune G., Negro L., Spina C.
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, 2013 In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the
A. Berlinet +19 more
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Journal of Mathematical Analysis and Applications, 2011 AbstractFix strictly increasing right continuous functions with left limits and periodic increments, Wi:R→R, i=1,…,d, and let W(x)=∑i=1dWi(xi) for x∈Rd. We construct the W-Sobolev spaces, which consist of functions f having weak generalized gradients ∇Wf=(∂W1f,…,∂Wdf).
Alexandre B. Simas, Fábio J. Valentim
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Final State Problem for the Dirac-Klein-Gordon Equations in Two Space Dimensions
Abstract and Applied Analysis, 2013 We study the final state problem for the Dirac-Klein-Gordon equations (DKG) in two space dimensions. We prove that if the nonresonance mass condition is satisfied, then the wave operator for DKG is well defined from a neighborhood at the origin in lower ...
Masahiro Ikeda
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INVERSE SPECTRAL PROBLEMS FOR STURM–LIOUVILLE OPERATORS WITH SINGULAR POTENTIALS. IV. POTENTIALS IN THE SOBOLEV SPACE SCALE [PDF]
Proceedings of the Edinburgh Mathematical Society, 2004 We solve the inverse spectral problems for the class of Sturm–Liouville operators with singular real-valued potentials from the Sobolev space $W^{s-1}_2(0,1)$, $s\in[0,1]$.
R. Hryniv, Y. Mykytyuk
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On the constants for multiplication in Sobolev spaces
Advances in Applied Mathematics, 2006 For n > d/2, the Sobolev (Bessel potential) space H^n(R^d, C) is known to be a Banach algebra with its standard norm || ||_n and the pointwise product; so, there is a best constant K_{n d} such that || f g ||_{n} <= K_{n d} || f ||_{n} || g ||_{n} for all f, g in this space.
C. Morosi, L. Pizzocchero
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