Weighted Sobolev Spaces on Curves [PDF]
Journal of Approximation Theory, 2002 In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.
Venancio Alvarez +3 more
openaire +5 more sources
Sobolev capacity on the space W1, p(⋅)(ℝn) [PDF]
Journal of Function Spaces and Applications, 2003 We define Sobolev capacity on the generalized Sobolev space W1, p(⋅)(ℝn). It is a Choquet capacity provided that the variable exponent p:ℝn→[1,∞) is bounded away from 1 and ∞.
Petteri Harjulehto +3 more
doaj +2 more sources
Journal of Inequalities and Applications, 2011 Let , the authors introduce in this paper a class of the hypersingular Marcinkiewicz integrals along surface with variable kernels defined by , where with .
Ruiying Wei, Yin Li
doaj +3 more sources
Clarkson’s Inequalities for Periodic Sobolev Space [PDF]
Учёные записки Казанского университета: Серия Физико-математические науки, 2016 The paper is devoted to developing the proof of Clarkson's inequalities for periodic functions belonging to the Sobolev space. The norm of the space has not been considered earlier.
I.V. Korytov
doaj +1 more source
Marine Anoxia and Ocean Acidification During the End‐Permian Extinction
Geophysical Monograph Series, Page 325-340., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Ying Cui +4 more
wiley +5 more sources
High‐Pressure Na‐Ca Carbonates in the Deep Carbon Cycle
Geophysical Monograph Series, Page 127-136., 2020 This book is Open Access. A digital copy can be downloaded for free from Wiley Online Library.
Explores the behavior of carbon in minerals, melts, and fluids under extreme conditions
Carbon trapped in diamonds and carbonate-bearing rocks in subduction zones are examples of the continuing exchange of substantial carbon ...
Sergey Rashchenko +2 more
wiley +6 more sources
Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation. [PDF]
, 2012 The periodic KdV equation arises from a Hamiltonian system with infinite-dimensional phase space L^2(T). Bourgain has shown that there exists a Gibbs measure \nu on balls in the phase space such that the Cauchy problem for KdV is well posed on the ...
Blower, Gordon
core +5 more sources
Logarithmic Sobolev inequalities and spectral concentration for the cubic Shrödinger equation [PDF]
, 2014 The nonlinear Schr\"odinger equation $\NLSE(p, \beta)$, $-iu_t=-u_{xx}+\beta \vert u\vert^{p-2} u=0$, arises from a Hamiltonian on infinite-dimensional phase space $\Lp^2(\mT)$. For $p\leq 6$, Bourgain (Comm. Math. Phys. 166 (1994), 1--26) has shown that
Doust, Ian +2 more
core +4 more sources
Algorithms and error bounds for multivariate piecewise constant approximation [PDF]
, 2011 We review the surprisingly rich theory of approximation of functions of many vari- ables by piecewise constants. This covers for example the Sobolev-Poincar´e inequalities, parts of the theory of nonlinear approximation, Haar wavelets and tree ...
Davydov, Oleg
core +4 more sources
Completeness properties of Sobolev metrics on the space of curves [PDF]
, 2014 We study completeness properties of Sobolev metrics on the space of immersed curves and on the shape space of unparametrized curves. We show that Sobolev metrics of order $n\geq 2$ are metrically complete on the space $\mathcal I^n(S^1,\mathbb R^d)$ of ...
Bruveris, M
core +7 more sources