The square root problem for elliptic operators a survey

1990 ◽  
pp. 122-140 ◽  
Author(s):  
Alan McIntosh
Keyword(s):  
Elliptic Operators ◽  
Square Root

The Solution of the Kato Square Root Problem for Second Order Elliptic Operators on \Bbb R n

2002 ◽  
Vol 156 (2) ◽  
pp. 633 ◽  
Author(s):  
Pascal Auscher ◽  
Steve Hofmann ◽  
Michael Lacey ◽  
Alan McIntosh ◽  
Ph. Tchamitchian
Keyword(s):  
Elliptic Operators ◽  
Second Order ◽  
Square Root ◽  
Second Order Elliptic Operators ◽  
Kato Square Root Problem

The Kato square root problem for higher order elliptic operators and systems on $ \Bbb R^n $

2001 ◽  
Vol 1 (4) ◽  
pp. 361-385 ◽  
Author(s):  
Pascal Auscher ◽  
Steve Hofmann ◽  
Alan McIntosh ◽  
Philippe Tchamitchian
Keyword(s):  
Higher Order ◽  
Elliptic Operators ◽  
Square Root ◽  
Kato Square Root Problem

The commutator of the Kato square root for second order elliptic operators on ℝ n

2016 ◽  
Vol 32 (10) ◽  
pp. 1121-1144 ◽  
Author(s):  
Yan Ping Chen ◽  
Yong Ding ◽  
Steve Hofmann
Keyword(s):  
Elliptic Operators ◽  
Second Order ◽  
Square Root ◽  
Second Order Elliptic Operators

VLSI module for high-performance multiply, square root and divide

1992 ◽  
Vol 139 (6) ◽  
pp. 505 ◽  
Author(s):  
S.E. McQuillan ◽  
J.V. McCanny
Keyword(s):  
High Performance ◽  
Square Root

Erratum: Realisation of irrational immitances containing a square root

1987 ◽  
Vol 134 (2) ◽  
pp. 94
Author(s):  
J.S. Visser
Keyword(s):  
Square Root

A computer-assisted proof method of the invertibility to elliptic operators

2014 ◽  
Vol 1 ◽  
pp. 816-819
Author(s):  
Akitoshi Takayasu ◽  
Shin'ichi Oishi
Keyword(s):  
Elliptic Operators ◽  
Computer Assisted ◽  
Computer Assisted Proof

Fast Montgomery-Like Square Root Computation for All Trinomials

2019 ◽  
Vol E102.A (1) ◽  
pp. 307-309 ◽  
Author(s):  
Yin LI ◽  
Yu ZHANG ◽  
Xiaoli GUO
Keyword(s):  
Square Root

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Adjoint Operator ◽  
Integral Kernel ◽  
Mathematical Finance ◽  
Elliptic Operators ◽  
Complete Analysis ◽  
Time Behavior ◽  
Degenerate Elliptic Operators ◽  
Regularity Properties ◽  
Degenerate Elliptic ◽  
Mathematical Foundations

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

Sign in / Sign up

Export Citation Format

Share Document