A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients

Paul M. N. Feehan and Camelia Pop

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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.

Date: 2011-12, Revised 2013-08
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Published in Journal of Differential Equations 254 (2013), 4401-4445

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