Regularity in the obstacle problem for parabolic non-divergence operators of Hörmander type |
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Authors: | Marie Frentz |
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Institution: | Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, United Kingdom |
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Abstract: | In this paper we continue the study initiated in 15] concerning the obstacle problem for a class of parabolic non-divergence operators structured on a set of vector fields X={X1,…,Xq} in Rn with C∞-coefficients satisfying Hörmander?s finite rank condition, i.e., the rank of LieX1,…,Xq] equals n at every point in Rn. In 15] we proved, under appropriate assumptions on the operator and the obstacle, the existence and uniqueness of strong solutions to a general obstacle problem. The main result of this paper is that we establish further regularity, in the interior as well as at the initial state, of strong solutions. Compared to 15] we in this paper assume, in addition, that there exists a homogeneous Lie group G=(Rn,°,δλ) such that X1,…,Xq are left translation invariant on G and such that X1,…,Xq are δλ-homogeneous of degree one. |
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Keywords: | 35K70 35B65 35B44 35A09 |
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