We prove local a priori estimates inLp, 1<p<∞, for first-order linear operators that satisfy the Nirenberg-Treves condition (p) and whose coefficients have Lipschitz continuous derivatives of order one. When the number of variables is two, only Lipschitz continuity of the coefficients is assumed. This extends toLp spaces estimates that were previously known forp=2. Examples show that the regularity required from the coefficients is essentially minimal.
Lipschitz Function Lipschitz Continuity Principal Symbol Principal Type Local Solvability
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