Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations
Abstract
We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of solutions up to the portion of the boundary where the operator is degenerate. Degenerate-elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance, generators of diffusion processes arising in mathematical biology, and the study of porous media.
Keywords
Cite
@article{arxiv.1210.6727,
title = {Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations},
author = {Paul M. N. Feehan and Camelia Pop},
journal= {arXiv preprint arXiv:1210.6727},
year = {2016}
}
Comments
58 pages, 1 figure. To appear in the Journal of Differential Equations. Incorporates final galley proof corrections corresponding to published version