Estimates for Some Ultraparabolic Operators with Discontinuous Coefficients
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چکیده
Ž Ž . Nq 1. q z s x, t g R , where the principal part is uniformly elliptic on R , q F N, and the constant matrix B is upper triangular and such that the operator obtained by freezing the coefficients a at any point z g R Nq 1 is hypoelliptic. We prove i j 0 p Ž . local L -estimates for the derivatives u i, j s 1, . . . , q of a solution to the x x i j equation Lu s f , under the assumption that the coefficients a belong to i j Ž . the space VMO ‘‘vanishing mean oscillation’’ with respect to a suitable metric related to B. Q 1996 Academic Press, Inc.
منابع مشابه
A Gaussian upper bound for the fundamental solutions of a class of ultraparabolic equations ✩
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تاریخ انتشار 1995