Results 131 to 140 of about 5,040,927 (317)
Vector-valued Sobolev spaces based on Banach function spaces [PDF]
arXiv, 2020 It is known that for Banach valued functions there are several approaches to define a Sobolev class. We compare the usual definition via weak derivatives with the Reshetnyak-Sobolev space and with the Newtonian space; in particular, we provide sufficient conditions when all three agree.
arxiv
Sobolev and Hardy-Littlewood-Sobolev inequalities: duality and fast diffusion [PDF]
Math. Res. Lett. 18, 6 (2011) 1037-1050, 2011 In the euclidean space, Sobolev and Hardy-Littlewood-Sobolev inequalities can be related by duality. In this paper, we investigate how to relate these inequalities using the flow of a fast diffusion equation in dimension $d\ge3$. The main consequence is an improvement of Sobolev's inequality when $d\ge5$, which involves the various terms of the dual ...
arxiv
On the density of continuous functions in variable exponent Sobolev space
, 2007 In this article we give new conditions for the density of continuous or smooth functions in variable exponent Sobolev spaces. Our first result combines the previously known sufficient conditions, a monotony condition by Edmunds and Rákosńık and a ...
P. Hst
semanticscholar +2 more sources
The Cauchy problem for nonlinear wave equations in the Sobolev space of critical order
, 1997 We show the local in time solvability of the Cauchy problem for nonlinear wave equations in the Sobolev space of critical order with nonlinear term of exponential type.
M. Nakamura, T. Ozawa
semanticscholar +1 more source
Clifford Analysis on Orlicz-Sobolev Spaces [PDF]
arXiv, 2014 In this article we develop few of the analogous theoretical results of Clifford analysis over Orlicz-Sobolev spaces and study mapping properties of the Dirac operator and the Teodorescu transform over these function spaces. We also get analogous decomposition results of Clifford valued Orlicz spaces and the generalized Orlicz-Sobolev spaces.
arxiv
Proceedings of the Edinburgh Mathematical Society, 1997 We study the initial value problem to the Davey-Stewartson system for the elliptic-hyperbolic case in the usual Sobolev space. We prove local existence and uniqueness H5/2 with a condition such that the L2 norm of the data is sufficiently small.
N. Hayashi, Hitoshi Hirata
semanticscholar +1 more source
Journal of Function Spaces, 2014 We introduce a new space QK(∂D) of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on K such that QK(∂D)=BMO(∂D), as well as a general criterion on weight ...
Jizhen Zhou
doaj +1 more source
On the identity of Morrey-Calkin and Schauder-Sobolev spaces [PDF]
, 1956 P. Szeptycki
openalex +1 more source
Sobolev space projections in strictly pseudoconvex domains
, 1985 . The orthogonal projection from a Sobolev space WS(Q) onto the subspace of holomorphic functions is studied. This analogue of the Bergman projection is shown to satisfy regularity estimates in higher Sobolev norms when ß is a smooth bounded strictly ...
H. Boas
semanticscholar +1 more source
Hyponormal Toeplitz Operators on the Dirichlet Spaces
Abstract and Applied Analysis, 2013 We completely characterize the hyponormality of bounded Toeplitz operators with Sobolev symbols on the Dirichlet space and the harmonic Dirichlet space.
Puyu Cui, Yufeng Lu
doaj +1 more source