Abstract
We consider a class of Kolmogorov equation
in a bounded open domain \({\Omega \subset \mathbb{R}^{N+1}}\), where the coefficients matrix (a ij (z)) is symmetric uniformly positive definite on \({\mathbb{R}^{p_0} (1 \leq p_0 < N)}\). We obtain interior W 1,p (1 < p < ∞) regularity and Hölder continuity of weak solutions to the equation under the assumption that coefficients a ij (z) belong to the \({VMO_L\cap L^\infty}\) and \({({b_{ij}})_{N \times N}}\) is a constant matrix such that the frozen operator \({L_{z_0}}\) is hypoelliptic.
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This work was supported by the National Natural Science Foundation of China (Grant Nos.11271299 and 11001221.
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Zhu, M., Niu, P. Interior W 1,p Regularity and Hölder Continuity of Weak Solutions to a Class of Divergence Kolmogorov Equations with Discontinuous Coefficients. Milan J. Math. 81, 317–346 (2013). https://doi.org/10.1007/s00032-013-0203-5
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DOI: https://doi.org/10.1007/s00032-013-0203-5