Divergence Operator and Related Inequalities

2017 ◽  
Author(s):  
Gabriel Acosta ◽  
Ricardo G. Durán
Keyword(s):  
Divergence Operator

scholarly journals Solutions of the divergence operator on John domains

2006 ◽  
Vol 206 (2) ◽  
pp. 373-401 ◽  
Author(s):  
Gabriel Acosta ◽  
Ricardo G. Durán ◽  
María A. Muschietti
Keyword(s):  
Divergence Operator ◽  
John Domains

scholarly journals Divergence operator and Poincaré inequalities on arbitrary bounded domains

2010 ◽  
Vol 55 (8-10) ◽  
pp. 795-816 ◽  
Author(s):  
Ricardo Duran ◽  
Maria-Amelia Muschietti ◽  
Emmanuel Russ ◽  
Philippe Tchamitchian
Keyword(s):  
Bounded Domains ◽  
Poincaré Inequalities ◽  
Divergence Operator ◽  
Poincare Inequalities

scholarly journals Sobolev spaces with respect to a weighted Gaussian measure in infinite dimensions

2019 ◽  
Vol 22 (04) ◽  
pp. 1950026 ◽  
Author(s):  
S. Ferrari
Keyword(s):  
Banach Space ◽  
Sobolev Spaces ◽  
Gaussian Measure ◽  
Separable Banach Space ◽  
Positive Function ◽  
Infinite Dimensions ◽  
Sobolev Function ◽  
Gradient Operator ◽  
Divergence Operator ◽  
Sobolev Functions

Let [Formula: see text] be a separable Banach space endowed with a nondegenerate centered Gaussian measure [Formula: see text] and let [Formula: see text] be a positive function on [Formula: see text] such that [Formula: see text] and [Formula: see text] for some [Formula: see text] and [Formula: see text]. In this paper, we introduce and study Sobolev spaces with respect to the weighted Gaussian measure [Formula: see text]. We obtain results regarding the divergence operator (i.e. the adjoint in [Formula: see text] of the gradient operator along the Cameron–Martin space) and the trace of Sobolev functions on hypersurfaces [Formula: see text], where [Formula: see text] is a suitable version of a Sobolev function.

Transport-Elliptic Estimates

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Elliptic Equation ◽  
Transport Equation ◽  
Transport Properties ◽  
Error Term ◽  
Main Lemma ◽  
Spatial Derivative ◽  
Material Derivative ◽  
Divergence Operator ◽  
Spatial Derivatives ◽  
Elliptic Estimates

This chapter solves the underdetermined, elliptic equation ∂ⱼQsuperscript jl = Usuperscript l and Qsuperscript jl = Qsuperscript lj (Equation 1069) in order to eliminate the error term in the parametrix. For the proof of the Main Lemma, estimates for Q and the material derivative as well as its spatial derivatives are derived. The chapter finds a solution to Equation (1069) with good transport properties by solving it via a Transport equation obtained by commuting the divergence operator with the material derivative. It concludes by showing the solutions, spatial derivative estimates, and material derivative estimates for the Transport-Elliptic equation, as well as cutting off the solution to the Transport-Elliptic equation.

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