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

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  • 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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    File URL: http://arxiv.org/pdf/1112.4824
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    Paper provided by arXiv.org in its series Papers with number 1112.4824.

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    Date of creation: Dec 2011
    Date of revision: Aug 2013
    Publication status: Published in Journal of Differential Equations 254 (2013), 4401-4445
    Handle: RePEc:arx:papers:1112.4824

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    1. Marc Atlan, 2006. "Localizing Volatilities," Papers math/0604316, arXiv.org.
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