The observation of the $\barν_e$ energy spectrum from a supernova burst can provide constraints on neutrino oscillations. We derive formulas for adiabatic oscillations of supernova antineutrinos for a variety of 3- and 4-neutrino mixing schemes and mass hierarchies which are consistent with the LSND evidence for $\barν_μ\to \barν_e$ oscillations. Finally, we explore the constraints on these models and LSND given by the supernova SN1987A $\barν_e$'s observed by the Kamiokande-2 and IMB-3 detectors.

8 pages, 3 figures. Changes with respect to original version: appendix added; minor changes in text, figures, references