Results 51 to 60 of about 5,040,927 (317)
On a class of fractional differential equations in a Sobolev space
, 2012 This article is concerned with the study of the existence and uniqueness of solutions to a class of fractional differential equations in a Sobolev space. The fractional time derivative is considered in Riemann–Liouville sense.
G. Mophou, G. N’Guérékata
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Uhlenbeck’s Decomposition in Sobolev and Morrey–Sobolev Spaces [PDF]
Results in Mathematics, 2018 We present a self-contained proof of Uhlenbeck's decomposition theorem for $ \in L^p(\mathbb{B}^n,so(m)\otimes ^1\mathbb{R}^n)$ for $p\in (1,n)$ with Sobolev type estimates in the case $p \in[n/2,n)$ and Morrey-Sobolev type estimates in the case $p\in (1,n/2)$.
Anna Zatorska-Goldstein +1 more
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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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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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Sobolev spaces on hypergroups Gelfand pairs [PDF]
arXiv, 2023 This paper introduces Sobolev spaces over Gelfand pairs in the framework of hypergroups. The Sobolev spaces in question are constructed from the Fourier transform on hypergroup Gelfand pairs. Mainly, the paper focuses on the investigation of Sobolev embedding results.
arxiv
, 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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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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, 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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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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