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Title: Estimates for Dirichlet-to-Neumann Maps as Integro-differential Operators
Some linear integro-differential operators have old and classical representations as the Dirichlet-to-Neumann operators for linear elliptic equations, such as the 1/2-Laplacian or the generator of the boundary process of a reflected diffusion. In this work, we make some extensions of this theory to the case of a nonlinear Dirichlet-to-Neumann mapping that is constructed using a solution to a fully nonlinear elliptic equation in a given domain, mapping Dirichlet data to its normal derivative of the resulting solution. Here we begin the process of giving detailed information about the Lévy measures that will result from the integro-differential representation of the Dirichlet-to-Neumann mapping. We provide new results about both linear and nonlinear Dirichlet-to-Neumann mappings. Information about the Lévy measures is important if one hopes to use recent advancements of the integro-differential theory to study problems involving Dirichlet-to-Neumann mappings.  more » « less
Award ID(s):
1700307 1665285 1700094
NSF-PAR ID:
10097955
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Potential analysis
ISSN:
1572-929X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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