It was shown in [4, 14] that a bounded solution of the heat equation in a half-space which becomes zero at some time must be identically zero, even though no assumptions are made on the boundary values of the solutions. In a recent example, Luis Escauriaza showed that this statement fails if the half-space is replaced by cones with opening angle smaller than 90°. Here we show that the result remains true for cones with opening angle larger than 110°.
Bibliographical noteFunding Information:
L. L. is supported in part by Louise T. Dosdall fellowship and Doctoral Dissertation Fellowship. V. S. is supported in part by NSF grant DMS 0800908.
- Backward uniqueness
- Cone domain
- Heat equation
- Parabolic equations