scholarly journals Liouville Principles and a Large-Scale Regularity Theory for Random Elliptic Operators on the Half-Space

2017 ◽  
Vol 49 (1) ◽  
pp. 82-114 ◽  
Author(s):  
Julian Fischer ◽  
Claudia Raithel
Keyword(s):  
Half Space ◽  
Large Scale ◽  
Regularity Theory ◽  
Elliptic Operators

scholarly journals A Regularity Theory for Random Elliptic Operators

2020 ◽  
Vol 88 (1) ◽  
pp. 99-170 ◽  
Author(s):  
Antoine Gloria ◽  
Stefan Neukamm ◽  
Felix Otto
Keyword(s):  
Regularity Theory ◽  
Elliptic Operators

Fast Multipole Boundary Element Method for 3-D Full- and Half-Space Acoustic Wave Problems

2009 ◽  
Author(s):  
Yijun Liu ◽  
Milind Bapat
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Half Space ◽  
Large Scale ◽  
Fast Multipole ◽  
Wave Problems ◽  
Acoustic Bem ◽  
Element Method

In this paper, the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 3-D full- and half-space domains will be discussed. First, the fast multipole BEM formulations will be presented and then improvements to the formulations and algorithms will be discussed. Examples with large-scale acoustic BEM models, with the DOFs above 2 millions and solved on desktop PCs, will be presented to demonstrate the potential of the fast multipole BEM for modeling large-scale structural acoustic problems.

scholarly journals Higher-Order Parabolic Equations with VMO Assumptions and General Boundary Conditions with Variable Leading Coefficients

2018 ◽  
Vol 2020 (7) ◽  
pp. 2114-2144 ◽  
Author(s):  
Hongjie Dong ◽  
Chiara Gallarati
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Parabolic Equations ◽  
Higher Order ◽  
Elliptic Operators ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Elliptic And Parabolic Equations ◽  
Boundary Operators ◽  
Higher Order Parabolic Equations

Abstract We prove weighted mixed $L_{p}(L_{q})$-estimates, with $p,q\in (1,\infty )$, and the corresponding solvability results for higher-order elliptic and parabolic equations on the half space ${\mathbb{R}}^{d+1}_{+}$ and on general $C^{2m-1,1}$ domains with general boundary conditions, which satisfy the Lopatinskii–Shapiro condition. We assume that the elliptic operators A have leading coefficients that are in the class of vanishing mean oscillations both in the time and the space variables and that the boundary operators have variable leading coefficients. The proofs are based on and generalize the estimates recently obtained by the authors in [6].

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