A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients
Abstract
Motivated by applications to probability and mathematical finance, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable and which become degenerate along the boundary of the half-space. We establish existence and uniqueness of solutions in weighted Holder spaces which incorporate both the degeneracy at the boundary and the unboundedness of the coefficients. In our companion article [arXiv:1211.4636], we apply the main result of this article to show that the martingale problem associated with a degenerate-elliptic partial differential operator is well-posed in the sense of Stroock and Varadhan.
Keywords
Cite
@article{arxiv.1112.4824,
title = {A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients},
author = {Paul M. N. Feehan and Camelia Pop},
journal= {arXiv preprint arXiv:1112.4824},
year = {2016}
}
Comments
42 pages; corresponds to Part 1 of our previous article [arxiv.org:1112.4824v1]. Incorporates final galley proof corrections corresponding to published version