scholarly journals Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators

2006 ◽  
Vol 195 (1-3) ◽  
pp. 26-64 ◽  
Author(s):  
C. Soize
Keyword(s):  
Random Fields ◽  
Differential Operators ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Non Gaussian

scholarly journals Stochastic elliptic operators defined by non-Gaussian random fields with uncertain spectrum

2021 ◽  
Vol 105 (0) ◽  
pp. 113-136
Author(s):  
C. Soize
Keyword(s):  
Random Fields ◽  
Elliptic Boundary ◽  
Positive Definite Matrix ◽  
Gaussian Random Fields ◽  
Positive Definite ◽  
Elliptic Operators ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
3D Space ◽  
Non Gaussian

This paper presents a construction and the analysis of a class of non-Gaussian positive-definite matrix-valued homogeneous random fields with uncertain spectral measure for stochastic elliptic operators. Then the stochastic elliptic boundary value problem in a bounded domain of the 3D-space is introduced and analyzed for stochastic homogenization.

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Sign in / Sign up

Export Citation Format

Share Document