[引用][C] On local regularity of Schrödinger equations
It is a well-known factthat, if V is a real and time-independent potential which belongs to L
(R") with p> n/2, the solution of (1-1) defines a continuous flow in H (R"), the Sobolev space
of functions in LZ (R") with s derivatives in LZ (R") and-2< s< 2. It is alsoeasy to see that
equation (1-1) is time reversible. Hence no global regularization of the initial data
concerning Sobolev spaces can be expected. However, it was established in [CS1],[Sj], and
IV1] that solutions of (1-1) in the free case (ie V 0) have locally 1/2 derivative more than the …
(R") with p> n/2, the solution of (1-1) defines a continuous flow in H (R"), the Sobolev space
of functions in LZ (R") with s derivatives in LZ (R") and-2< s< 2. It is alsoeasy to see that
equation (1-1) is time reversible. Hence no global regularization of the initial data
concerning Sobolev spaces can be expected. However, it was established in [CS1],[Sj], and
IV1] that solutions of (1-1) in the free case (ie V 0) have locally 1/2 derivative more than the …
It is a well-known factthat, if V is a real and time-independent potential which belongs to L (R") with p> n/2, the solution of (1-1) defines a continuous flow in H (R"), the Sobolev space of functions in LZ (R") with s derivatives in LZ (R") and-2< s< 2. It is alsoeasy to see that equation (1-1) is time reversible. Hence no global regularization of the initial data concerning Sobolev spaces can be expected. However, it was established in [CS1],[Sj], and IV1] that solutions of (1-1) in the free case (ie V 0) have locally 1/2 derivative more than the initial data for almost every time.
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