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arXiv · 1112.4824

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

Paul M. N. Feehan·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.

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Paul M. N. Feehan, Camelia Pop. 2013-08-08. A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients. https://doi.org/10.1016/j.jde.2013.03.006

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