A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients
AbstractMotivated 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1112.4824.
Date of creation: Dec 2011
Date of revision: Aug 2013
Publication status: Published in Journal of Differential Equations 254 (2013), 4401-4445
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-03 (All new papers)
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