Oscillatory integrals and unique continuation for second order elliptic differential equations

A well-known counterexample (see [11]) indicates that the condition V E LPn2 is in the best possible nature. This counterexample, however, has to do loc with unique continuation from a point rather than from open sets as in Theorem 1.1. We hope to treat unique continuation from a point in a subsequent paper. Results of this type for constant coefficient operators were obtained by Sawyer [14] for low dimensions and Jerison and Kenig [11] for general n. There was a lot of previous work, and we refer the reader to [11, 14] for further references. Also, Jerison and Kenig proved the stronger result that there is unique continuation from a point for constant coefficient operators. For variable coefficient operators our results improve one of H6rmander [8] which says that there is unique continuation from open sets for solutions to (1.1)