scholarly journals Weighted elliptic estimates for a mixed boundary system related to the Dirichlet-Neumann operator on a corner domain

2019 ◽  
Vol 39 (10) ◽  
pp. 6039-6067
Author(s):  
Mei Ming ◽  
Keyword(s):  
Mixed Boundary ◽  
Boundary System ◽  
Neumann Operator ◽  
Elliptic Estimates

scholarly journals Elliptic estimates for the Dirichlet–Neumann operator on a corner domain

2017 ◽  
Vol 104 (3-4) ◽  
pp. 103-166 ◽  
Author(s):  
Mei Ming ◽  
Chao Wang
Keyword(s):  
Neumann Operator ◽  
Elliptic Estimates

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

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