scholarly journals Square function estimates on layer potentials for higher-order elliptic equations

2017 ◽  
Vol 290 (16) ◽  
pp. 2459-2511 ◽  
Author(s):  
Ariel Barton ◽  
Steve Hofmann ◽  
Svitlana Mayboroda
Keyword(s):  
Elliptic Equations ◽  
Higher Order ◽  
Square Function ◽  
Layer Potentials ◽  
Square Function Estimates

scholarly journals Nontangential Estimates on Layer Potentials and the Neumann Problem for Higher-Order Elliptic Equations

2020 ◽  
Author(s):  
Ariel Barton ◽  
Steve Hofmann ◽  
Svitlana Mayboroda
Keyword(s):  
Neumann Problem ◽  
Elliptic Equations ◽  
Divergence Form ◽  
Higher Order ◽  
Elliptic Operators ◽  
Layer Potentials ◽  
The Neumann Problem

Abstract We solve the Neumann problem, with nontangential estimates, for higher-order divergence form elliptic operators with variable $t$-independent coefficients. Our results are accompanied by nontangential estimates on higher-order layer potentials.

scholarly journals Bounds on layer potentials with rough inputs for higher order elliptic equations

2019 ◽  
Vol 119 (3) ◽  
pp. 613-653 ◽  
Author(s):  
Ariel Barton ◽  
Steve Hofmann ◽  
Svitlana Mayboroda
Keyword(s):  
Elliptic Equations ◽  
Higher Order ◽  
Layer Potentials

scholarly journals EIGENVALUE ESTIMATES FOR HIGHER ORDER ELLIPTIC EQUATIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 267-278
Author(s):  
HSU-TUNG KU ◽  
MEI-CHIN KU ◽  
XIN-MIN ZHANG
Keyword(s):  
Lower Bound ◽  
Elliptic Equations ◽  
Eigenvalue Problems ◽  
Higher Order ◽  
Bounded Domains ◽  
Dirichlet Eigenvalue ◽  
Eigenvalue Estimates

In this paper, we obtain good lower bound estimates of eigenvalues for various Dirichlet eigenvalue problems of higher order elliptic equations on bounded domains in $\mathbb{R}^n$.

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