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A note on the boundedness of solutions of linear parabolic equations

1962
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Proceedings of the American Mathematical Society
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Hartman and Wintner [l] obtained a Sturmian comparison theorem for self-adjoint second order elliptic equations of the form (1) Z -( aa-) in a bounded domain B with boundary dB. In this note, their method is slightly modified to prove the following theorem. Denote by D the semi-infinite cylinder {(x, /):xG-B,/>0},by 7) its closure and by Dt the intersection of D with the half-space / ^ T. Suppose u = u(x) is a solution of equation (1) which is continuous in B the closure of B, vanishes on dB

doi:10.1090/s0002-9939-1962-0136867-0
fatcat:wzrdczuvenfahhld2x4yt3vxza